Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,4,Mod(111,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.111");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 448.j (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: |
Embedding invariants
Embedding label | 335.37 | ||
Character | 448.335 | ||
Dual form | 448.4.j.b.111.37 |
-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 on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
4.79702 | − | 4.79702i | 0.923188 | − | 0.923188i | −0.0740657 | − | 0.997253i | ||
0.997253 | + | 0.0740657i | ||||||||
0 | 0 | |||||||||
2.04624 | − | 2.04624i | 0.183021 | − | 0.183021i | −0.609650 | − | 0.792671i | ||
0.792671 | + | 0.609650i | ||||||||
0 | 0 | |||||||||
−13.3740 | + | 12.8115i | −0.722130 | + | 0.691757i | |||||
0 | 0 | |||||||||
− | 19.0229i | − | 0.704551i | |||||||
0 | 0 | |||||||||
−34.5515 | + | 34.5515i | −0.947061 | + | 0.947061i | −0.998668 | − | 0.0516064i | ||
0.0516064 | + | 0.998668i | ||||||||
0 | 0 | |||||||||
−7.32563 | − | 7.32563i | −0.156290 | − | 0.156290i | 0.624631 | − | 0.780920i | ||
−0.780920 | + | 0.624631i | ||||||||
0 | 0 | |||||||||
− | 19.6317i | − | 0.337926i | |||||||
0 | 0 | |||||||||
133.707i | 1.90758i | 0.300477 | + | 0.953789i | ||||||
−0.300477 | + | 0.953789i | ||||||||
0 | 0 | |||||||||
13.6735 | − | 13.6735i | 0.165100 | − | 0.165100i | −0.619722 | − | 0.784822i | ||
0.784822 | + | 0.619722i | ||||||||
0 | 0 | |||||||||
−2.69841 | + | 125.613i | −0.0280401 | + | 1.30528i | |||||
0 | 0 | |||||||||
−129.773 | −1.17650 | −0.588250 | − | 0.808679i | ||||||
−0.588250 | + | 0.808679i | ||||||||
0 | 0 | |||||||||
116.626i | 0.933006i | |||||||||
0 | 0 | |||||||||
38.2664 | + | 38.2664i | 0.272755 | + | 0.272755i | |||||
0 | 0 | |||||||||
85.7909 | − | 85.7909i | 0.549344 | − | 0.549344i | −0.376907 | − | 0.926251i | ||
0.926251 | + | 0.376907i | ||||||||
0 | 0 | |||||||||
−239.073 | −1.38512 | −0.692560 | − | 0.721360i | ||||||
−0.692560 | + | 0.721360i | ||||||||
0 | 0 | |||||||||
331.489i | 1.74863i | |||||||||
0 | 0 | |||||||||
−1.15105 | + | 53.5820i | −0.00555893 | + | 0.258772i | |||||
0 | 0 | |||||||||
−50.7975 | − | 50.7975i | −0.225704 | − | 0.225704i | 0.585191 | − | 0.810895i | ||
−0.810895 | + | 0.585191i | ||||||||
0 | 0 | |||||||||
−70.2824 | −0.288569 | |||||||||
0 | 0 | |||||||||
118.276 | 0.450527 | 0.225264 | − | 0.974298i | ||||||
0.225264 | + | 0.974298i | ||||||||
0 | 0 | |||||||||
75.4750 | − | 75.4750i | 0.267671 | − | 0.267671i | −0.560490 | − | 0.828161i | ||
0.828161 | + | 0.560490i | ||||||||
0 | 0 | |||||||||
−38.9254 | − | 38.9254i | −0.128948 | − | 0.128948i | |||||
0 | 0 | |||||||||
−169.043 | −0.524625 | −0.262313 | − | 0.964983i | ||||||
−0.262313 | + | 0.964983i | ||||||||
0 | 0 | |||||||||
14.7299 | − | 342.684i | 0.0429442 | − | 0.999077i | |||||
0 | 0 | |||||||||
641.398 | + | 641.398i | 1.76105 | + | 1.76105i | |||||
0 | 0 | |||||||||
482.264 | + | 482.264i | 1.24989 | + | 1.24989i | 0.955769 | + | 0.294118i | ||
0.294118 | + | 0.955769i | ||||||||
0 | 0 | |||||||||
141.401i | 0.346665i | |||||||||
0 | 0 | |||||||||
− | 131.184i | − | 0.304837i | |||||||
0 | 0 | |||||||||
−285.231 | − | 285.231i | −0.629389 | − | 0.629389i | 0.318525 | − | 0.947914i | ||
−0.947914 | + | 0.318525i | ||||||||
0 | 0 | |||||||||
−313.070 | − | 313.070i | −0.657124 | − | 0.657124i | 0.297575 | − | 0.954699i | ||
−0.954699 | + | 0.297575i | ||||||||
0 | 0 | |||||||||
243.712 | + | 254.413i | 0.487378 | + | 0.508778i | |||||
0 | 0 | |||||||||
−29.9800 | −0.0572086 | |||||||||
0 | 0 | |||||||||
58.2711 | + | 58.2711i | 0.106253 | + | 0.106253i | 0.758235 | − | 0.651982i | ||
−0.651982 | + | 0.758235i | ||||||||
0 | 0 | |||||||||
−622.523 | + | 622.523i | −1.08613 | + | 1.08613i | |||||
0 | 0 | |||||||||
374.109 | 0.625331 | 0.312666 | − | 0.949863i | ||||||
0.312666 | + | 0.949863i | ||||||||
0 | 0 | |||||||||
610.003 | 0.978020 | 0.489010 | − | 0.872278i | ||||||
0.489010 | + | 0.872278i | ||||||||
0 | 0 | |||||||||
559.457 | + | 559.457i | 0.861340 | + | 0.861340i | |||||
0 | 0 | |||||||||
19.4359 | − | 904.751i | 0.0287652 | − | 1.33904i | |||||
0 | 0 | |||||||||
− | 460.899i | − | 0.656395i | −0.944609 | − | 0.328198i | ||||
0.944609 | − | 0.328198i | ||||||||
0 | 0 | |||||||||
880.748 | 1.20816 | |||||||||
0 | 0 | |||||||||
−875.405 | + | 875.405i | −1.15769 | + | 1.15769i | −0.172717 | + | 0.984971i | ||
−0.984971 | + | 0.172717i | ||||||||
0 | 0 | |||||||||
273.598 | + | 273.598i | 0.349128 | + | 0.349128i | |||||
0 | 0 | |||||||||
− | 823.082i | − | 1.01430i | |||||||
0 | 0 | |||||||||
−633.231 | −0.754184 | −0.377092 | − | 0.926176i | ||||||
−0.377092 | + | 0.926176i | ||||||||
0 | 0 | |||||||||
191.826 | + | 4.12080i | 0.220976 | + | 0.00474700i | |||||
0 | 0 | |||||||||
−1146.84 | + | 1146.84i | −1.27873 | + | 1.27873i | |||||
0 | 0 | |||||||||
− | 55.9584i | − | 0.0604338i | |||||||
0 | 0 | |||||||||
946.138i | 0.990368i | 0.868788 | + | 0.495184i | ||||||
−0.868788 | + | 0.495184i | ||||||||
0 | 0 | |||||||||
657.269 | + | 657.269i | 0.667253 | + | 0.667253i | |||||
0 | 0 | |||||||||
141.100 | − | 141.100i | 0.139010 | − | 0.139010i | −0.634178 | − | 0.773187i | ||
0.773187 | + | 0.634178i | ||||||||
0 | 0 | |||||||||
891.445i | 0.852784i | 0.904539 | + | 0.426392i | ||||||
−0.904539 | + | 0.426392i | ||||||||
0 | 0 | |||||||||
251.512 | + | 262.556i | 0.233763 | + | 0.244027i | |||||
0 | 0 | |||||||||
727.560 | − | 727.560i | 0.657345 | − | 0.657345i | −0.297406 | − | 0.954751i | ||
0.954751 | + | 0.297406i | ||||||||
0 | 0 | |||||||||
−1136.70 | + | 1136.70i | −0.998867 | + | 0.998867i | −0.999999 | − | 0.00113245i | ||
0.00113245 | + | 0.999999i | ||||||||
0 | 0 | |||||||||
−487.353 | −0.416735 | |||||||||
0 | 0 | |||||||||
−556.606 | −0.463373 | −0.231686 | − | 0.972791i | ||||||
−0.231686 | + | 0.972791i | ||||||||
0 | 0 | |||||||||
−265.546 | + | 265.546i | −0.215325 | + | 0.215325i | |||||
0 | 0 | |||||||||
−139.355 | + | 139.355i | −0.110114 | + | 0.110114i | |||||
0 | 0 | |||||||||
−1713.00 | − | 1788.21i | −1.31958 | − | 1.37752i | |||||
0 | 0 | |||||||||
− | 1056.61i | − | 0.793849i | |||||||
0 | 0 | |||||||||
567.373 | − | 567.373i | 0.415921 | − | 0.415921i | |||||
0 | 0 | |||||||||
494.425 | + | 494.425i | 0.353781 | + | 0.353781i | |||||
0 | 0 | |||||||||
1588.68i | 1.11002i | 0.831843 | + | 0.555011i | ||||||
−0.831843 | + | 0.555011i | ||||||||
0 | 0 | |||||||||
− | 724.111i | − | 0.494220i | |||||||
0 | 0 | |||||||||
−1500.21 | + | 1500.21i | −1.00057 | + | 1.00057i | −0.000565274 | 1.00000i | |||
−1.00000 | 0.000565274i | |||||||||
0 | 0 | |||||||||
−7.69157 | + | 358.047i | −0.00501461 | + | 0.233433i | |||||
0 | 0 | |||||||||
156.605 | 0.0998399 | |||||||||
0 | 0 | |||||||||
− | 2259.10i | − | 1.40882i | −0.709795 | − | 0.704408i | ||||
0.709795 | − | 0.704408i | ||||||||
0 | 0 | |||||||||
2145.82 | + | 2145.82i | 1.30940 | + | 1.30940i | 0.921850 | + | 0.387547i | ||
0.387547 | + | 0.921850i | ||||||||
0 | 0 | |||||||||
−810.901 | + | 810.901i | −0.484328 | + | 0.484328i | |||||
0 | 0 | |||||||||
506.223 | 0.296031 | |||||||||
0 | 0 | |||||||||
− | 351.098i | − | 0.201083i | |||||||
0 | 0 | |||||||||
−1573.20 | − | 1714.52i | −0.882690 | − | 0.961982i | |||||
0 | 0 | |||||||||
−1085.99 | − | 1085.99i | −0.597100 | − | 0.597100i | 0.342440 | − | 0.939540i | ||
−0.939540 | + | 0.342440i | ||||||||
0 | 0 | |||||||||
−257.765 | −0.138918 | −0.0694590 | − | 0.997585i | ||||||
−0.0694590 | + | 0.997585i | ||||||||
0 | 0 | |||||||||
2543.50 | 1.34399 | |||||||||
0 | 0 | |||||||||
−489.200 | + | 489.200i | −0.253507 | + | 0.253507i | |||||
0 | 0 | |||||||||
−1532.56 | − | 1532.56i | −0.779053 | − | 0.779053i | 0.200617 | − | 0.979670i | ||
−0.979670 | + | 0.200617i | ||||||||
0 | 0 | |||||||||
4626.86 | 2.30776 | |||||||||
0 | 0 | |||||||||
1735.59 | − | 1662.59i | 0.849586 | − | 0.813852i | |||||
0 | 0 | |||||||||
177.457 | + | 177.457i | 0.0852729 | + | 0.0852729i | 0.748457 | − | 0.663184i | ||
−0.663184 | + | 0.748457i | ||||||||
0 | 0 | |||||||||
678.306 | + | 678.306i | 0.320037 | + | 0.320037i | |||||
0 | 0 | |||||||||
− | 1722.29i | − | 0.798054i | −0.916939 | − | 0.399027i | ||||
0.916939 | − | 0.399027i | ||||||||
0 | 0 | |||||||||
− | 2089.67i | − | 0.951147i | |||||||
0 | 0 | |||||||||
−260.108 | − | 260.108i | −0.116322 | − | 0.116322i | |||||
0 | 0 | |||||||||
1795.20 | + | 1795.20i | 0.788939 | + | 0.788939i | 0.981320 | − | 0.192381i | ||
−0.192381 | + | 0.981320i | ||||||||
0 | 0 | |||||||||
−1494.15 | − | 1559.76i | −0.645414 | − | 0.673752i | |||||
0 | 0 | |||||||||
−2736.52 | −1.16209 | |||||||||
0 | 0 | |||||||||
953.910 | + | 953.910i | 0.398316 | + | 0.398316i | 0.877639 | − | 0.479323i | ||
−0.479323 | + | 0.877639i | ||||||||
0 | 0 | |||||||||
−1780.34 | + | 1780.34i | −0.731114 | + | 0.731114i | −0.970840 | − | 0.239727i | ||
0.239727 | + | 0.970840i | ||||||||
0 | 0 | |||||||||
−3003.61 | −1.21330 | |||||||||
0 | 0 | |||||||||
−207.888 | −0.0826173 | |||||||||
0 | 0 | |||||||||
−4619.79 | − | 4619.79i | −1.80659 | − | 1.80659i | |||||
0 | 0 | |||||||||
−1002.03 | − | 21.5256i | −0.385645 | − | 0.00828442i | |||||
0 | 0 | |||||||||
− | 2064.00i | − | 0.781916i | −0.920409 | − | 0.390958i | ||||
0.920409 | − | 0.390958i | ||||||||
0 | 0 | |||||||||
1142.67 | 0.426172 | 0.213086 | − | 0.977033i | ||||||
0.213086 | + | 0.977033i | ||||||||
0 | 0 | |||||||||
−143.815 | + | 143.815i | −0.0528143 | + | 0.0528143i | |||||
0 | 0 | |||||||||
837.511 | + | 837.511i | 0.302894 | + | 0.302894i | 0.842145 | − | 0.539251i | ||
−0.539251 | + | 0.842145i | ||||||||
0 | 0 | |||||||||
− | 2165.33i | − | 0.771338i | −0.922637 | − | 0.385669i | ||||
0.922637 | − | 0.385669i | ||||||||
0 | 0 | |||||||||
559.056 | 0.196183 | |||||||||
0 | 0 | |||||||||
−48.2590 | + | 2246.48i | −0.0166853 | + | 0.776710i | |||||
0 | 0 | |||||||||
242.021 | − | 242.021i | 0.0824561 | − | 0.0824561i | |||||
0 | 0 | |||||||||
2468.65i | 0.828904i | |||||||||
0 | 0 | |||||||||
944.877i | 0.312720i | |||||||||
0 | 0 | |||||||||
−130.423 | − | 130.423i | −0.0425531 | − | 0.0425531i | 0.685510 | − | 0.728063i | ||
−0.728063 | + | 0.685510i | ||||||||
0 | 0 | |||||||||
1794.61 | − | 1794.61i | 0.577298 | − | 0.577298i | |||||
0 | 0 | |||||||||
− | 308.880i | − | 0.0979789i | |||||||
0 | 0 | |||||||||
3197.37 | − | 3062.89i | 1.00024 | − | 0.958167i | |||||
0 | 0 | |||||||||
2926.20 | − | 2926.20i | 0.902896 | − | 0.902896i | |||||
0 | 0 | |||||||||
979.491 | − | 979.491i | 0.298134 | − | 0.298134i | |||||
0 | 0 | |||||||||
−1221.92 | −0.366933 | −0.183466 | − | 0.983026i | ||||||
−0.183466 | + | 0.983026i | ||||||||
0 | 0 | |||||||||
2218.56 | 0.657351 | |||||||||
0 | 0 | |||||||||
3515.16 | − | 3515.16i | 1.02780 | − | 1.02780i | 0.0281934 | − | 0.999602i | ||
0.999602 | − | 0.0281934i | ||||||||
0 | 0 | |||||||||
3345.39 | − | 3345.39i | 0.965369 | − | 0.965369i | −0.0340515 | − | 0.999420i | ||
0.999420 | + | 0.0340515i | ||||||||
0 | 0 | |||||||||
−4246.88 | − | 4433.34i | −1.20963 | − | 1.26274i | |||||
0 | 0 | |||||||||
− | 537.847i | − | 0.151225i | −0.997137 | − | 0.0756127i | ||||
0.997137 | − | 0.0756127i | ||||||||
0 | 0 | |||||||||
−345.902 | + | 345.902i | −0.0960177 | + | 0.0960177i | |||||
0 | 0 | |||||||||
−2210.95 | − | 2210.95i | −0.605976 | − | 0.605976i | |||||
0 | 0 | |||||||||
− | 6403.30i | − | 1.73303i | −0.499149 | − | 0.866516i | ||||
0.499149 | − | 0.866516i | ||||||||
0 | 0 | |||||||||
− | 1648.67i | − | 0.440664i | −0.975425 | − | 0.220332i | ||||
0.975425 | − | 0.220332i | ||||||||
0 | 0 | |||||||||
3191.77 | − | 3191.77i | 0.842603 | − | 0.842603i | |||||
0 | 0 | |||||||||
−671.072 | − | 731.354i | −0.174993 | − | 0.190712i | |||||
0 | 0 | |||||||||
−200.333 | −0.0516069 | |||||||||
0 | 0 | |||||||||
8398.68i | 2.13753i | |||||||||
0 | 0 | |||||||||
3775.90 | + | 3775.90i | 0.949534 | + | 0.949534i | 0.998786 | − | 0.0492528i | ||
−0.0492528 | + | 0.998786i | ||||||||
0 | 0 | |||||||||
4483.84 | − | 4483.84i | 1.11422 | − | 1.11422i | |||||
0 | 0 | |||||||||
2624.91 | 0.644620 | |||||||||
0 | 0 | |||||||||
6959.86i | 1.68928i | 0.535337 | + | 0.844638i | ||||||
−0.535337 | + | 0.844638i | ||||||||
0 | 0 | |||||||||
1330.16 | + | 28.5745i | 0.319120 | + | 0.00685534i | |||||
0 | 0 | |||||||||
−1631.99 | − | 1631.99i | −0.387041 | − | 0.387041i | |||||
0 | 0 | |||||||||
4461.40 | 1.04602 | 0.523008 | − | 0.852328i | ||||||
0.523008 | + | 0.852328i | ||||||||
0 | 0 | |||||||||
1973.66 | 0.457512 | |||||||||
0 | 0 | |||||||||
−3037.62 | + | 3037.62i | −0.696253 | + | 0.696253i | |||||
0 | 0 | |||||||||
−2252.15 | − | 2252.15i | −0.510469 | − | 0.510469i | 0.404201 | − | 0.914670i | ||
−0.914670 | + | 0.404201i | ||||||||
0 | 0 | |||||||||
−6670.05 | −1.49512 | −0.747559 | − | 0.664196i | ||||||
−0.747559 | + | 0.664196i | ||||||||
0 | 0 | |||||||||
939.960 | − | 900.425i | 0.208384 | − | 0.199620i | |||||
0 | 0 | |||||||||
−4029.60 | − | 4029.60i | −0.883614 | − | 0.883614i | |||||
0 | 0 | |||||||||
−1517.50 | − | 1517.50i | −0.329161 | − | 0.329161i | 0.523106 | − | 0.852267i | ||
−0.852267 | + | 0.523106i | ||||||||
0 | 0 | |||||||||
4547.85i | 0.975888i | |||||||||
0 | 0 | |||||||||
− | 559.278i | − | 0.118732i | −0.998236 | − | 0.0593661i | ||||
0.998236 | − | 0.0593661i | ||||||||
0 | 0 | |||||||||
−25.8379 | − | 25.8379i | −0.00542721 | − | 0.00542721i | 0.704388 | − | 0.709815i | ||
−0.709815 | + | 0.704388i | ||||||||
0 | 0 | |||||||||
−268.434 | − | 268.434i | −0.0557917 | − | 0.0557917i | |||||
0 | 0 | |||||||||
−1581.83 | + | 1515.30i | −0.325339 | + | 0.311655i | |||||
0 | 0 | |||||||||
−12964.7 | −2.63885 | |||||||||
0 | 0 | |||||||||
4538.65 | + | 4538.65i | 0.914296 | + | 0.914296i | |||||
0 | 0 | |||||||||
−3862.53 | + | 3862.53i | −0.770142 | + | 0.770142i | −0.978131 | − | 0.207989i | ||
0.207989 | + | 0.978131i | ||||||||
0 | 0 | |||||||||
−1167.30 | −0.230383 | |||||||||
0 | 0 | |||||||||
−2644.33 | −0.516631 | |||||||||
0 | 0 | |||||||||
950.667 | + | 950.667i | 0.183875 | + | 0.183875i | |||||
0 | 0 | |||||||||
−42.4561 | + | 1976.36i | −0.00812999 | + | 0.378456i | |||||
0 | 0 | |||||||||
− | 1353.72i | − | 0.256664i | |||||||
0 | 0 | |||||||||
−1281.23 | −0.240535 | |||||||||
0 | 0 | |||||||||
−2044.42 | + | 2044.42i | −0.380069 | + | 0.380069i | −0.871127 | − | 0.491058i | ||
0.491058 | + | 0.871127i | ||||||||
0 | 0 | |||||||||
4276.28 | + | 4276.28i | 0.787279 | + | 0.787279i | |||||
0 | 0 | |||||||||
9371.35i | 1.70868i | 0.519711 | + | 0.854342i | ||||||
−0.519711 | + | 0.854342i | ||||||||
0 | 0 | |||||||||
−8978.95 | −1.62147 | −0.810735 | − | 0.585413i | ||||||
−0.810735 | + | 0.585413i | ||||||||
0 | 0 | |||||||||
1019.28 | + | 21.8962i | 0.182318 | + | 0.00391655i | |||||
0 | 0 | |||||||||
−1767.75 | + | 1767.75i | −0.313207 | + | 0.313207i | −0.846151 | − | 0.532944i | ||
0.532944 | + | 0.846151i | ||||||||
0 | 0 | |||||||||
5928.41i | 1.04052i | |||||||||
0 | 0 | |||||||||
− | 6980.25i | − | 1.21371i | |||||||
0 | 0 | |||||||||
1828.24 | + | 1828.24i | 0.314942 | + | 0.314942i | |||||
0 | 0 | |||||||||
854.357 | − | 854.357i | 0.145819 | − | 0.145819i | |||||
0 | 0 | |||||||||
10905.6i | 1.84428i | |||||||||
0 | 0 | |||||||||
2260.78 | − | 2165.69i | 0.378848 | − | 0.362913i | |||||
0 | 0 | |||||||||
−4730.32 | + | 4730.32i | −0.785504 | + | 0.785504i | −0.980754 | − | 0.195250i | ||
0.195250 | + | 0.980754i | ||||||||
0 | 0 | |||||||||
−966.314 | + | 966.314i | −0.159020 | + | 0.159020i | |||||
0 | 0 | |||||||||
238.473 | 0.0388931 | |||||||||
0 | 0 | |||||||||
1717.91 | 0.277688 | 0.138844 | − | 0.990314i | ||||||
0.138844 | + | 0.990314i | ||||||||
0 | 0 | |||||||||
−2670.05 | + | 2670.05i | −0.427780 | + | 0.427780i | |||||
0 | 0 | |||||||||
8260.32 | − | 8260.32i | 1.31179 | − | 1.31179i | |||||
0 | 0 | |||||||||
4193.30 | + | 4771.78i | 0.660108 | + | 0.751171i | |||||
0 | 0 | |||||||||
2547.66i | 0.397570i | |||||||||
0 | 0 | |||||||||
7793.80 | − | 7793.80i | 1.20574 | − | 1.20574i | 0.233352 | − | 0.972392i | ||
0.972392 | − | 0.233352i | ||||||||
0 | 0 | |||||||||
4211.57 | + | 4211.57i | 0.645960 | + | 0.645960i | 0.952014 | − | 0.306054i | ||
−0.306054 | + | 0.952014i | ||||||||
0 | 0 | |||||||||
− | 560.652i | − | 0.0852574i | |||||||
0 | 0 | |||||||||
7172.87i | 1.08151i | 0.841180 | + | 0.540755i | ||||||
−0.841180 | + | 0.540755i | ||||||||
0 | 0 | |||||||||
765.516 | − | 765.516i | 0.114449 | − | 0.114449i | |||||
0 | 0 | |||||||||
−16795.4 | − | 360.798i | −2.48993 | − | 0.0534887i | |||||
0 | 0 | |||||||||
12810.1 | 1.88326 | 0.941630 | − | 0.336650i | ||||||
0.941630 | + | 0.336650i | ||||||||
0 | 0 | |||||||||
6485.07i | 0.945484i | |||||||||
0 | 0 | |||||||||
−5068.60 | − | 5068.60i | −0.732872 | − | 0.732872i | |||||
0 | 0 | |||||||||
1248.21 | − | 1248.21i | 0.178998 | − | 0.178998i | |||||
0 | 0 | |||||||||
−5502.08 | −0.782578 | −0.391289 | − | 0.920268i | ||||||
−0.391289 | + | 0.920268i | ||||||||
0 | 0 | |||||||||
− | 2249.95i | − | 0.317419i | |||||||
0 | 0 | |||||||||
−12628.3 | − | 271.282i | −1.76720 | − | 0.0379630i | |||||
0 | 0 | |||||||||
−5026.12 | − | 5026.12i | −0.697702 | − | 0.697702i | 0.266213 | − | 0.963914i | ||
−0.963914 | + | 0.266213i | ||||||||
0 | 0 | |||||||||
4743.53 | 0.653213 | |||||||||
0 | 0 | |||||||||
−1256.94 | −0.171713 | |||||||||
0 | 0 | |||||||||
−6001.11 | + | 6001.11i | −0.813342 | + | 0.813342i | −0.985133 | − | 0.171792i | ||
0.171792 | + | 0.985133i | ||||||||
0 | 0 | |||||||||
7620.96 | + | 7620.96i | 1.02476 | + | 1.02476i | |||||
0 | 0 | |||||||||
12452.4 | 1.66133 | 0.830665 | − | 0.556773i | ||||||
0.830665 | + | 0.556773i | ||||||||
0 | 0 | |||||||||
−1811.57 | − | 1891.11i | −0.239808 | − | 0.250337i | |||||
0 | 0 | |||||||||
−1435.75 | − | 1435.75i | −0.188588 | − | 0.188588i | |||||
0 | 0 | |||||||||
7568.58 | + | 7568.58i | 0.986483 | + | 0.986483i | 0.999910 | − | 0.0134265i | ||
−0.0134265 | + | 0.999910i | ||||||||
0 | 0 | |||||||||
− | 17351.6i | − | 2.24426i | |||||||
0 | 0 | |||||||||
14393.1i | 1.84742i | |||||||||
0 | 0 | |||||||||
−943.111 | − | 943.111i | −0.120134 | − | 0.120134i | |||||
0 | 0 | |||||||||
−746.476 | − | 746.476i | −0.0943692 | − | 0.0943692i | 0.658346 | − | 0.752715i | ||
−0.752715 | + | 0.658346i | ||||||||
0 | 0 | |||||||||
1680.66 | + | 1754.46i | 0.210873 | + | 0.220132i | |||||
0 | 0 | |||||||||
8402.79 | 1.04642 | 0.523211 | − | 0.852203i | ||||||
0.523211 | + | 0.852203i | ||||||||
0 | 0 | |||||||||
1751.36 | + | 1751.36i | 0.216480 | + | 0.216480i | |||||
0 | 0 | |||||||||
1802.22 | − | 1802.22i | 0.221119 | − | 0.221119i | |||||
0 | 0 | |||||||||
3510.26 | 0.427511 | |||||||||
0 | 0 | |||||||||
−8430.15 | −1.01918 | −0.509589 | − | 0.860418i | ||||||
−0.509589 | + | 0.860418i | ||||||||
0 | 0 | |||||||||
−10837.0 | − | 10837.0i | −1.30060 | − | 1.30060i | |||||
0 | 0 | |||||||||
7468.95 | + | 160.448i | 0.889886 | + | 0.0191165i | |||||
0 | 0 | |||||||||
3582.58i | 0.423764i | |||||||||
0 | 0 | |||||||||
20587.1 | 2.41764 | |||||||||
0 | 0 | |||||||||
8672.14 | − | 8672.14i | 1.01113 | − | 1.01113i | 0.0111887 | − | 0.999937i | ||
0.999937 | − | 0.0111887i | ||||||||
0 | 0 | |||||||||
10398.8 | + | 10398.8i | 1.20382 | + | 1.20382i | 0.972997 | + | 0.230818i | ||
0.230818 | + | 0.972997i | ||||||||
0 | 0 | |||||||||
3215.68i | 0.369625i | |||||||||
0 | 0 | |||||||||
−15593.7 | −1.77978 | |||||||||
0 | 0 | |||||||||
8197.92 | + | 176.108i | 0.929099 | + | 0.0199589i | |||||
0 | 0 | |||||||||
2428.36 | − | 2428.36i | 0.273293 | − | 0.273293i | |||||
0 | 0 | |||||||||
12243.6i | 1.36834i | 0.729322 | + | 0.684170i | ||||||
−0.729322 | + | 0.684170i | ||||||||
0 | 0 | |||||||||
− | 8787.77i | − | 0.975320i | −0.873034 | − | 0.487660i | ||||
0.873034 | − | 0.487660i | ||||||||
0 | 0 | |||||||||
−1684.22 | − | 1684.22i | −0.185638 | − | 0.185638i | |||||
0 | 0 | |||||||||
−1774.44 | + | 1774.44i | −0.194240 | + | 0.194240i | |||||
0 | 0 | |||||||||
6163.76i | 0.670115i | 0.942198 | + | 0.335057i | ||||||
−0.942198 | + | 0.335057i | ||||||||
0 | 0 | |||||||||
−6518.83 | − | 280.204i | −0.703901 | − | 0.0302564i | |||||
0 | 0 | |||||||||
−705.371 | + | 705.371i | −0.0756505 | + | 0.0756505i | −0.743920 | − | 0.668269i | ||
0.668269 | + | 0.743920i | ||||||||
0 | 0 | |||||||||
−1295.74 | + | 1295.74i | −0.138032 | + | 0.138032i | |||||
0 | 0 | |||||||||
−10419.1 | −1.10247 | |||||||||
0 | 0 | |||||||||
1808.14 | 0.190048 | 0.0950240 | − | 0.995475i | ||||||
0.0950240 | + | 0.995475i | ||||||||
0 | 0 | |||||||||
−4086.62 | + | 4086.62i | −0.426677 | + | 0.426677i | |||||
0 | 0 | |||||||||
−1236.51 | + | 1236.51i | −0.128247 | + | 0.128247i | |||||
0 | 0 | |||||||||
400.954 | − | 384.089i | 0.0413121 | − | 0.0395745i | |||||
0 | 0 | |||||||||
− | 13173.0i | − | 1.34838i | −0.738560 | − | 0.674188i | ||||
0.738560 | − | 0.674188i | ||||||||
0 | 0 | |||||||||
−5116.51 | + | 5116.51i | −0.520301 | + | 0.520301i | |||||
0 | 0 | |||||||||
−2780.05 | − | 2780.05i | −0.280867 | − | 0.280867i | 0.552588 | − | 0.833455i | ||
−0.833455 | + | 0.552588i | ||||||||
0 | 0 | |||||||||
3630.01i | 0.364365i | 0.983265 | + | 0.182182i | ||||||
−0.983265 | + | 0.182182i | ||||||||
0 | 0 | |||||||||
4693.41i | 0.468068i | |||||||||
0 | 0 | |||||||||
39.0209 | − | 39.0209i | 0.00386654 | − | 0.00386654i | −0.705171 | − | 0.709037i | ||
0.709037 | + | 0.705171i | ||||||||
0 | 0 | |||||||||
−1525.86 | − | 32.7786i | −0.150230 | − | 0.00322723i | |||||
0 | 0 | |||||||||
−14703.4 | −1.43842 | |||||||||
0 | 0 | |||||||||
5215.55i | 0.507001i | |||||||||
0 | 0 | |||||||||
1594.68 | + | 1594.68i | 0.154040 | + | 0.154040i | |||||
0 | 0 | |||||||||
9174.04 | − | 9174.04i | 0.880609 | − | 0.880609i | |||||
0 | 0 | |||||||||
1088.16 | 0.103798 | 0.0518990 | − | 0.998652i | ||||||
0.0518990 | + | 0.998652i | ||||||||
0 | 0 | |||||||||
744.247i | 0.0705504i | |||||||||
0 | 0 | |||||||||
350.181 | − | 16301.1i | 0.0329892 | − | 1.53567i | |||||
0 | 0 | |||||||||
1936.03 | + | 1936.03i | 0.181259 | + | 0.181259i | |||||
0 | 0 | |||||||||
17740.1 | 1.65068 | 0.825339 | − | 0.564638i | ||||||
0.825339 | + | 0.564638i | ||||||||
0 | 0 | |||||||||
1702.53 | 0.157446 | |||||||||
0 | 0 | |||||||||
−5821.10 | + | 5821.10i | −0.535036 | + | 0.535036i | −0.922067 | − | 0.387031i | ||
0.387031 | + | 0.922067i | ||||||||
0 | 0 | |||||||||
11470.9 | + | 11470.9i | 1.04792 | + | 1.04792i | |||||
0 | 0 | |||||||||
2689.86 | 0.244243 | |||||||||
0 | 0 | |||||||||
−5003.34 | + | 4792.90i | −0.451571 | + | 0.432577i | |||||
0 | 0 | |||||||||
−4283.85 | − | 4283.85i | −0.384312 | − | 0.384312i | 0.488341 | − | 0.872653i | ||
−0.872653 | + | 0.488341i | ||||||||
0 | 0 | |||||||||
−8261.88 | − | 8261.88i | −0.736753 | − | 0.736753i | |||||
0 | 0 | |||||||||
743.585i | 0.0659142i | 0.999457 | + | 0.0329571i | ||||||
−0.999457 | + | 0.0329571i | ||||||||
0 | 0 | |||||||||
− | 577.449i | − | 0.0508834i | |||||||
0 | 0 | |||||||||
−10024.2 | − | 10024.2i | −0.878087 | − | 0.878087i | |||||
0 | 0 | |||||||||
6189.71 | + | 6189.71i | 0.539006 | + | 0.539006i | 0.923237 | − | 0.384231i | ||
−0.384231 | + | 0.923237i | ||||||||
0 | 0 | |||||||||
−8158.20 | + | 7815.06i | −0.706258 | + | 0.676552i | |||||
0 | 0 | |||||||||
1046.47 | 0.0900638 | |||||||||
0 | 0 | |||||||||
1824.11 | + | 1824.11i | 0.156078 | + | 0.156078i | |||||
0 | 0 | |||||||||
5840.68 | − | 5840.68i | 0.496852 | − | 0.496852i | |||||
0 | 0 | |||||||||
17223.2 | 1.45668 | |||||||||
0 | 0 | |||||||||
11779.3 | 0.990521 | 0.495260 | − | 0.868745i | ||||||
0.495260 | + | 0.868745i | ||||||||
0 | 0 | |||||||||
1261.69 | + | 1261.69i | 0.105488 | + | 0.105488i | 0.757881 | − | 0.652393i | ||
−0.652393 | + | 0.757881i | ||||||||
0 | 0 | |||||||||
−14649.7 | − | 314.705i | −1.21784 | − | 0.0261616i | |||||
0 | 0 | |||||||||
− | 31965.8i | − | 2.64222i | |||||||
0 | 0 | |||||||||
4673.97 | 0.384151 | |||||||||
0 | 0 | |||||||||
−5425.92 | + | 5425.92i | −0.443437 | + | 0.443437i | |||||
0 | 0 | |||||||||
−866.447 | − | 866.447i | −0.0704127 | − | 0.0704127i | |||||
0 | 0 | |||||||||
− | 2977.53i | − | 0.240616i | |||||||
0 | 0 | |||||||||
9151.86 | 0.735441 | |||||||||
0 | 0 | |||||||||
11331.3 | + | 12349.2i | 0.905517 | + | 0.986858i | |||||
0 | 0 | |||||||||
3180.80 | − | 3180.80i | 0.252778 | − | 0.252778i | −0.569330 | − | 0.822109i | ||
0.822109 | + | 0.569330i | ||||||||
0 | 0 | |||||||||
17080.7i | 1.34991i | |||||||||
0 | 0 | |||||||||
4651.94i | 0.365628i | |||||||||
0 | 0 | |||||||||
2706.48 | + | 2706.48i | 0.211555 | + | 0.211555i | 0.804928 | − | 0.593373i | ||
−0.593373 | + | 0.804928i | ||||||||
0 | 0 | |||||||||
−5955.50 | + | 5955.50i | −0.462977 | + | 0.462977i | |||||
0 | 0 | |||||||||
− | 2346.12i | − | 0.181394i | |||||||
0 | 0 | |||||||||
5904.82 | + | 6164.09i | 0.454066 | + | 0.474003i | |||||
0 | 0 | |||||||||
−997.242 | + | 997.242i | −0.0762713 | + | 0.0762713i | |||||
0 | 0 | |||||||||
−1976.55 | + | 1976.55i | −0.150358 | + | 0.150358i | −0.778278 | − | 0.627920i | ||
0.627920 | + | 0.778278i | ||||||||
0 | 0 | |||||||||
−1105.80 | −0.0836682 | |||||||||
0 | 0 | |||||||||
−44322.5 | −3.33565 | |||||||||
0 | 0 | |||||||||
1969.01 | − | 1969.01i | 0.147396 | − | 0.147396i | −0.629558 | − | 0.776954i | ||
0.776954 | + | 0.629558i | ||||||||
0 | 0 | |||||||||
−1138.95 | + | 1138.95i | −0.0848071 | + | 0.0848071i | |||||
0 | 0 | |||||||||
−11779.2 | + | 11283.7i | −0.872448 | + | 0.835752i | |||||
0 | 0 | |||||||||
12025.5i | 0.886004i | 0.896521 | + | 0.443002i | ||||||
−0.896521 | + | 0.443002i | ||||||||
0 | 0 | |||||||||
3067.62 | − | 3067.62i | 0.224826 | − | 0.224826i | −0.585701 | − | 0.810527i | ||
0.810527 | + | 0.585701i | ||||||||
0 | 0 | |||||||||
−9901.06 | − | 9901.06i | −0.721855 | − | 0.721855i | |||||
0 | 0 | |||||||||
− | 15134.8i | − | 1.09768i | |||||||
0 | 0 | |||||||||
− | 4574.91i | − | 0.330080i | −0.986287 | − | 0.165040i | ||||
0.986287 | − | 0.165040i | ||||||||
0 | 0 | |||||||||
5481.42 | − | 5481.42i | 0.393437 | − | 0.393437i | |||||
0 | 0 | |||||||||
492.431 | − | 22923.0i | 0.0351626 | − | 1.63684i | |||||
0 | 0 | |||||||||
−33325.9 | −2.36744 | |||||||||
0 | 0 | |||||||||
570.306i | 0.0403064i | |||||||||
0 | 0 | |||||||||
−1826.09 | − | 1826.09i | −0.128400 | − | 0.128400i | 0.639986 | − | 0.768386i | ||
−0.768386 | + | 0.639986i | ||||||||
0 | 0 | |||||||||
−3268.95 | + | 3268.95i | −0.228684 | + | 0.228684i | |||||
0 | 0 | |||||||||
8035.12 | 0.559257 | |||||||||
0 | 0 | |||||||||
− | 5705.55i | − | 0.395107i | −0.980292 | − | 0.197554i | ||||
0.980292 | − | 0.197554i | ||||||||
0 | 0 | |||||||||
−7164.31 | − | 153.904i | −0.493627 | − | 0.0106041i | |||||
0 | 0 | |||||||||
−10387.1 | − | 10387.1i | −0.712090 | − | 0.712090i | |||||
0 | 0 | |||||||||
−10497.7 | −0.716070 | −0.358035 | − | 0.933708i | ||||||
−0.358035 | + | 0.933708i | ||||||||
0 | 0 | |||||||||
−9375.74 | −0.636347 | −0.318173 | − | 0.948033i | ||||||
−0.318173 | + | 0.948033i | ||||||||
0 | 0 | |||||||||
1108.48 | − | 1108.48i | 0.0748606 | − | 0.0748606i | |||||
0 | 0 | |||||||||
−2162.09 | − | 2162.09i | −0.145291 | − | 0.145291i | |||||
0 | 0 | |||||||||
−5702.60 | −0.381320 | −0.190660 | − | 0.981656i | ||||||
−0.190660 | + | 0.981656i | ||||||||
0 | 0 | |||||||||
10544.9 | + | 11007.9i | 0.701646 | + | 0.732453i | |||||
0 | 0 | |||||||||
1238.34 | + | 1238.34i | 0.0819934 | + | 0.0819934i | |||||
0 | 0 | |||||||||
7424.25 | + | 7424.25i | 0.489172 | + | 0.489172i | 0.908045 | − | 0.418873i | ||
−0.418873 | + | 0.908045i | ||||||||
0 | 0 | |||||||||
− | 2321.96i | − | 0.152245i | |||||||
0 | 0 | |||||||||
− | 22808.8i | − | 1.48825i | −0.668043 | − | 0.744123i | ||||
0.668043 | − | 0.744123i | ||||||||
0 | 0 | |||||||||
15749.6 | + | 15749.6i | 1.02267 | + | 1.02267i | 0.999737 | + | 0.0229291i | ||
0.0229291 | + | 0.999737i | ||||||||
0 | 0 | |||||||||
−4965.94 | − | 4965.94i | −0.320896 | − | 0.320896i | |||||
0 | 0 | |||||||||
8468.86 | − | 8112.65i | 0.544619 | − | 0.521712i | |||||
0 | 0 | |||||||||
−12554.8 | −0.803507 | |||||||||
0 | 0 | |||||||||
4532.60 | + | 4532.60i | 0.288699 | + | 0.288699i | |||||
0 | 0 | |||||||||
6792.00 | − | 6792.00i | 0.430548 | − | 0.430548i | |||||
0 | 0 | |||||||||
7632.20 | 0.481510 | 0.240755 | − | 0.970586i | ||||||
0.240755 | + | 0.970586i | ||||||||
0 | 0 | |||||||||
−1251.29 | −0.0785689 | |||||||||
0 | 0 | |||||||||
3250.83 | + | 3250.83i | 0.203158 | + | 0.203158i | |||||
0 | 0 | |||||||||
−2618.28 | + | 2402.47i | −0.162857 | + | 0.149434i | |||||
0 | 0 | |||||||||
− | 7116.62i | − | 0.440578i | |||||||
0 | 0 | |||||||||
18811.7 | 1.15915 | 0.579576 | − | 0.814918i | ||||||
0.579576 | + | 0.814918i | ||||||||
0 | 0 | |||||||||
14360.3 | − | 14360.3i | 0.880740 | − | 0.880740i | −0.112869 | − | 0.993610i | ||
0.993610 | + | 0.112869i | ||||||||
0 | 0 | |||||||||
−1481.71 | − | 1481.71i | −0.0904529 | − | 0.0904529i | |||||
0 | 0 | |||||||||
13880.5i | 0.843430i | 0.906728 | + | 0.421715i | ||||||
−0.906728 | + | 0.421715i | ||||||||
0 | 0 | |||||||||
19710.4 | 1.19214 | |||||||||
0 | 0 | |||||||||
645.117 | − | 30030.6i | 0.0388389 | − | 1.80797i | |||||
0 | 0 | |||||||||
6926.86 | − | 6926.86i | 0.415113 | − | 0.415113i | −0.468402 | − | 0.883515i | ||
0.883515 | + | 0.468402i | ||||||||
0 | 0 | |||||||||
6139.59i | 0.366250i | |||||||||
0 | 0 | |||||||||
− | 11604.0i | − | 0.689065i | |||||||
0 | 0 | |||||||||
21306.6 | + | 21306.6i | 1.25947 | + | 1.25947i | 0.951348 | + | 0.308118i | ||
0.308118 | + | 0.951348i | ||||||||
0 | 0 | |||||||||
9192.89 | − | 9192.89i | 0.540941 | − | 0.540941i | −0.382864 | − | 0.923805i | ||
0.923805 | + | 0.382864i | ||||||||
0 | 0 | |||||||||
− | 9397.29i | − | 0.550468i | |||||||
0 | 0 | |||||||||
716.912 | + | 748.389i | 0.0418055 | + | 0.0436410i | |||||
0 | 0 | |||||||||
−11133.3 | + | 11133.3i | −0.646303 | + | 0.646303i | |||||
0 | 0 | |||||||||
−5861.59 | + | 5861.59i | −0.338748 | + | 0.338748i | |||||
0 | 0 | |||||||||
21634.1 | 1.24467 | |||||||||
0 | 0 | |||||||||
−24859.6 | −1.42388 | −0.711938 | − | 0.702242i | ||||||
−0.711938 | + | 0.702242i | ||||||||
0 | 0 | |||||||||
−4462.85 | + | 4462.85i | −0.254482 | + | 0.254482i | |||||
0 | 0 | |||||||||
−11098.7 | + | 11098.7i | −0.630070 | + | 0.630070i | −0.948086 | − | 0.318016i | ||
0.318016 | + | 0.948086i | ||||||||
0 | 0 | |||||||||
−12121.5 | − | 12653.7i | −0.685094 | − | 0.715175i | |||||
0 | 0 | |||||||||
− | 33724.7i | − | 1.89770i | |||||||
0 | 0 | |||||||||
5129.88 | − | 5129.88i | 0.287393 | − | 0.287393i | −0.548656 | − | 0.836048i | ||
0.836048 | + | 0.548656i | ||||||||
0 | 0 | |||||||||
−4622.66 | − | 4622.66i | −0.257844 | − | 0.257844i | |||||
0 | 0 | |||||||||
− | 32095.8i | − | 1.78243i | |||||||
0 | 0 | |||||||||
− | 7065.77i | − | 0.390688i | |||||||
0 | 0 | |||||||||
1243.53 | − | 1243.53i | 0.0684606 | − | 0.0684606i | −0.672047 | − | 0.740508i | ||
0.740508 | + | 0.672047i | ||||||||
0 | 0 | |||||||||
−17211.0 | − | 369.726i | −0.943420 | − | 0.0202666i | |||||
0 | 0 | |||||||||
8781.73 | 0.479295 | |||||||||
0 | 0 | |||||||||
15814.4i | 0.859416i | |||||||||
0 | 0 | |||||||||
−2580.07 | − | 2580.07i | −0.139609 | − | 0.139609i | |||||
0 | 0 | |||||||||
8513.11 | − | 8513.11i | 0.458681 | − | 0.458681i | −0.439541 | − | 0.898223i | ||
0.898223 | + | 0.439541i | ||||||||
0 | 0 | |||||||||
−1389.15 | −0.0745276 | |||||||||
0 | 0 | |||||||||
3318.60i | 0.177285i | |||||||||
0 | 0 | |||||||||
−79.3713 | + | 3694.78i | −0.00422216 | + | 0.196544i | |||||
0 | 0 | |||||||||
20499.4 | + | 20499.4i | 1.08585 | + | 1.08585i | 0.995950 | + | 0.0899043i | ||
0.0899043 | + | 0.995950i | ||||||||
0 | 0 | |||||||||
−8767.63 | −0.462464 | |||||||||
0 | 0 | |||||||||
31025.1 | 1.62959 | |||||||||
0 | 0 | |||||||||
1035.85 | − | 1035.85i | 0.0541801 | − | 0.0541801i | |||||
0 | 0 | |||||||||
−30716.8 | − | 30716.8i | −1.59991 | − | 1.59991i | |||||
0 | 0 | |||||||||
−14074.7 | −0.730037 | −0.365018 | − | 0.931000i | ||||||
−0.365018 | + | 0.931000i | ||||||||
0 | 0 | |||||||||
−11420.8 | − | 11922.2i | −0.589919 | − | 0.615821i | |||||
0 | 0 | |||||||||
−7908.69 | − | 7908.69i | −0.406815 | − | 0.406815i | |||||
0 | 0 | |||||||||
10005.4 | + | 10005.4i | 0.512541 | + | 0.512541i | |||||
0 | 0 | |||||||||
95.2264i | 0.00485798i | 0.999997 | + | 0.00242899i | ||||||
−0.999997 | + | 0.00242899i | ||||||||
0 | 0 | |||||||||
− | 6841.84i | − | 0.347602i | |||||||
0 | 0 | |||||||||
10091.6 | + | 10091.6i | 0.510602 | + | 0.510602i | |||||
0 | 0 | |||||||||
−13958.3 | − | 13958.3i | −0.703357 | − | 0.703357i | 0.261772 | − | 0.965130i | ||
−0.965130 | + | 0.261772i | ||||||||
0 | 0 | |||||||||
−6727.47 | − | 289.173i | −0.337614 | − | 0.0145120i | |||||
0 | 0 | |||||||||
−4026.71 | −0.201256 | |||||||||
0 | 0 | |||||||||
−22132.3 | − | 22132.3i | −1.10169 | − | 1.10169i | −0.994207 | − | 0.107485i | ||
−0.107485 | − | 0.994207i | ||||||||
0 | 0 | |||||||||
−961.004 | + | 961.004i | −0.0476428 | + | 0.0476428i | |||||
0 | 0 | |||||||||
5532.55 | 0.273176 | 0.136588 | − | 0.990628i | ||||||
0.136588 | + | 0.990628i | ||||||||
0 | 0 | |||||||||
−4444.40 | −0.218564 | |||||||||
0 | 0 | |||||||||
16652.7 | + | 16652.7i | 0.815651 | + | 0.815651i | |||||
0 | 0 | |||||||||
−409.266 | + | 19051.6i | −0.0199656 | + | 0.929412i | |||||
0 | 0 | |||||||||
36330.7i | 1.76528i | 0.470048 | + | 0.882641i | ||||||
−0.470048 | + | 0.882641i | ||||||||
0 | 0 | |||||||||
36226.2 | 1.75320 | |||||||||
0 | 0 | |||||||||
−527.449 | + | 527.449i | −0.0254250 | + | 0.0254250i | |||||
0 | 0 | |||||||||
15674.3 | + | 15674.3i | 0.752564 | + | 0.752564i | 0.974957 | − | 0.222393i | ||
−0.222393 | + | 0.974957i | ||||||||
0 | 0 | |||||||||
− | 43018.2i | − | 2.05726i | |||||||
0 | 0 | |||||||||
16656.7 | 0.793437 | 0.396718 | − | 0.917940i | ||||||
0.396718 | + | 0.917940i | ||||||||
0 | 0 | |||||||||
639.417 | − | 29765.2i | 0.0303387 | − | 1.41229i | |||||
0 | 0 | |||||||||
5204.62 | − | 5204.62i | 0.245978 | − | 0.245978i | |||||
0 | 0 | |||||||||
4179.00i | 0.196734i | |||||||||
0 | 0 | |||||||||
9190.37i | 0.430966i | 0.976508 | + | 0.215483i | ||||||
−0.976508 | + | 0.215483i | ||||||||
0 | 0 | |||||||||
33386.6 | + | 33386.6i | 1.55952 | + | 1.55952i | |||||
0 | 0 | |||||||||
−3285.14 | + | 3285.14i | −0.152857 | + | 0.152857i | −0.779393 | − | 0.626536i | ||
0.626536 | + | 0.779393i | ||||||||
0 | 0 | |||||||||
− | 27882.0i | − | 1.29233i | |||||||
0 | 0 | |||||||||
6517.88 | − | 6243.74i | 0.300937 | − | 0.288279i | |||||
0 | 0 | |||||||||
1617.24 | − | 1617.24i | 0.0743822 | − | 0.0743822i | |||||
0 | 0 | |||||||||
−12926.0 | + | 12926.0i | −0.592227 | + | 0.592227i | |||||
0 | 0 | |||||||||
6565.83 | 0.299672 | |||||||||
0 | 0 | |||||||||
−6271.96 | −0.285167 | |||||||||
0 | 0 | |||||||||
11875.1 | − | 11875.1i | 0.537867 | − | 0.537867i | −0.385035 | − | 0.922902i | ||
0.922902 | + | 0.385035i | ||||||||
0 | 0 | |||||||||
21401.5 | − | 21401.5i | 0.965668 | − | 0.965668i | |||||
0 | 0 | |||||||||
7444.08 | − | 7130.98i | 0.334616 | − | 0.320541i | |||||
0 | 0 | |||||||||
4586.87i | 0.205403i | |||||||||
0 | 0 | |||||||||
9467.67 | − | 9467.67i | 0.422369 | − | 0.422369i | |||||
0 | 0 | |||||||||
27267.4 | + | 27267.4i | 1.21187 | + | 1.21187i | 0.970411 | + | 0.241460i | ||
0.241460 | + | 0.970411i | ||||||||
0 | 0 | |||||||||
− | 22602.3i | − | 1.00076i | |||||||
0 | 0 | |||||||||
12045.9i | 0.531361i | |||||||||
0 | 0 | |||||||||
−21076.5 | + | 21076.5i | −0.926244 | + | 0.926244i | |||||
0 | 0 | |||||||||
149.375 | − | 6953.48i | 0.00654008 | − | 0.304445i | |||||
0 | 0 | |||||||||
−21607.3 | −0.942518 | |||||||||
0 | 0 | |||||||||
− | 37899.6i | − | 1.64707i | −0.567265 | − | 0.823535i | ||||
0.567265 | − | 0.823535i | ||||||||
0 | 0 | |||||||||
−2453.46 | − | 2453.46i | −0.106230 | − | 0.106230i | 0.651994 | − | 0.758224i | ||
−0.758224 | + | 0.651994i | ||||||||
0 | 0 | |||||||||
−31996.4 | + | 31996.4i | −1.38027 | + | 1.38027i | |||||
0 | 0 | |||||||||
726.238 | 0.0312135 | |||||||||
0 | 0 | |||||||||
− | 2064.01i | − | 0.0883850i | |||||||
0 | 0 | |||||||||
78.3895 | − | 3649.08i | 0.00334451 | − | 0.155689i | |||||
0 | 0 | |||||||||
−16123.1 | − | 16123.1i | −0.685385 | − | 0.685385i | 0.275823 | − | 0.961208i | ||
−0.961208 | + | 0.275823i | ||||||||
0 | 0 | |||||||||
−24632.9 | −1.04332 | −0.521658 | − | 0.853155i | ||||||
−0.521658 | + | 0.853155i | ||||||||
0 | 0 | |||||||||
−38660.1 | −1.63148 | |||||||||
0 | 0 | |||||||||
−1089.80 | + | 1089.80i | −0.0458236 | + | 0.0458236i | −0.729647 | − | 0.683824i | ||
0.683824 | + | 0.729647i | ||||||||
0 | 0 | |||||||||
4055.04 | + | 4055.04i | 0.169888 | + | 0.169888i | 0.786930 | − | 0.617042i | ||
−0.617042 | + | 0.786930i | ||||||||
0 | 0 | |||||||||
−14559.0 | −0.607755 | |||||||||
0 | 0 | |||||||||
45819.4 | + | 1969.49i | 1.90582 | + | 0.0819194i | |||||
0 | 0 | |||||||||
−3524.22 | − | 3524.22i | −0.146061 | − | 0.146061i | |||||
0 | 0 | |||||||||
−9148.46 | − | 9148.46i | −0.377798 | − | 0.377798i | |||||
0 | 0 | |||||||||
35349.1i | 1.45457i | 0.686335 | + | 0.727285i | ||||||
−0.686335 | + | 0.727285i | ||||||||
0 | 0 | |||||||||
9668.83i | 0.396442i | |||||||||
0 | 0 | |||||||||
−2682.87 | − | 2682.87i | −0.109612 | − | 0.109612i | |||||
0 | 0 | |||||||||
−4275.97 | − | 4275.97i | −0.174080 | − | 0.174080i | |||||
0 | 0 | |||||||||
13536.8 | + | 14131.2i | 0.549151 | + | 0.573263i | |||||
0 | 0 | |||||||||
−247.890 | −0.0100207 | |||||||||
0 | 0 | |||||||||
6592.13 | + | 6592.13i | 0.265541 | + | 0.265541i | |||||
0 | 0 | |||||||||
−28356.9 | + | 28356.9i | −1.13824 | + | 1.13824i | −0.149477 | + | 0.988765i | ||
−0.988765 | + | 0.149477i | ||||||||
0 | 0 | |||||||||
−1064.49 | −0.0425787 | |||||||||
0 | 0 | |||||||||
5617.28 | 0.223900 | 0.111950 | − | 0.993714i | ||||||
0.111950 | + | 0.993714i | ||||||||
0 | 0 | |||||||||
26923.7 | + | 26923.7i | 1.06941 | + | 1.06941i | 0.997404 | + | 0.0720059i | ||
0.0720059 | + | 0.997404i | ||||||||
0 | 0 | |||||||||
−319.158 | + | 14857.0i | −0.0126328 | + | 0.588066i | |||||
0 | 0 | |||||||||
− | 7764.09i | − | 0.306249i | −0.988207 | − | 0.153124i | ||||
0.988207 | − | 0.153124i | ||||||||
0 | 0 | |||||||||
7346.82 | 0.288785 | |||||||||
0 | 0 | |||||||||
−62191.9 | + | 62191.9i | −2.43616 | + | 2.43616i | |||||
0 | 0 | |||||||||
15924.8 | + | 15924.8i | 0.621646 | + | 0.621646i | |||||
0 | 0 | |||||||||
− | 853.745i | − | 0.0332124i | |||||||
0 | 0 | |||||||||
17998.3 | 0.697765 | |||||||||
0 | 0 | |||||||||
−12946.8 | − | 278.123i | −0.500207 | − | 0.0107455i | |||||
0 | 0 | |||||||||
15619.2 | − | 15619.2i | 0.601396 | − | 0.601396i | −0.339287 | − | 0.940683i | ||
0.940683 | + | 0.339287i | ||||||||
0 | 0 | |||||||||
37057.3i | 1.42197i | |||||||||
0 | 0 | |||||||||
45320.9i | 1.73314i | 0.499053 | + | 0.866571i | ||||||
−0.499053 | + | 0.866571i | ||||||||
0 | 0 | |||||||||
5998.33 | + | 5998.33i | 0.228607 | + | 0.228607i | 0.812110 | − | 0.583504i | ||
−0.583504 | + | 0.812110i | ||||||||
0 | 0 | |||||||||
−5599.59 | + | 5599.59i | −0.212687 | + | 0.212687i | |||||
0 | 0 | |||||||||
− | 25507.8i | − | 0.965578i | −0.875737 | − | 0.482789i | ||||
0.875737 | − | 0.482789i | ||||||||
0 | 0 | |||||||||
−20353.5 | − | 21247.1i | −0.767866 | − | 0.801581i | |||||
0 | 0 | |||||||||
−30431.2 | + | 30431.2i | −1.14420 | + | 1.14420i | |||||
0 | 0 | |||||||||
−2311.40 | + | 2311.40i | −0.0866158 | + | 0.0866158i | |||||
0 | 0 | |||||||||
3903.86 | 0.145801 | |||||||||
0 | 0 | |||||||||
9120.74 | 0.339501 | |||||||||
0 | 0 | |||||||||
−20510.3 | + | 20510.3i | −0.760907 | + | 0.760907i | |||||
0 | 0 | |||||||||
−64482.2 | + | 64482.2i | −2.38426 | + | 2.38426i | |||||
0 | 0 | |||||||||
9276.96 | + | 9684.29i | 0.341880 | + | 0.356891i | |||||
0 | 0 | |||||||||
7286.01i | 0.267619i | |||||||||
0 | 0 | |||||||||
26334.9 | − | 26334.9i | 0.964096 | − | 0.964096i | −0.0352818 | − | 0.999377i | ||
0.999377 | + | 0.0352818i | ||||||||
0 | 0 | |||||||||
−2684.13 | − | 2684.13i | −0.0979393 | − | 0.0979393i | |||||
0 | 0 | |||||||||
16395.8i | 0.596285i | 0.954521 | + | 0.298142i | ||||||
−0.954521 | + | 0.298142i | ||||||||
0 | 0 | |||||||||
− | 60493.1i | − | 2.19280i | |||||||
0 | 0 | |||||||||
−6146.11 | + | 6146.11i | −0.222059 | + | 0.222059i | |||||
0 | 0 | |||||||||
843.896 | − | 39283.9i | 0.0303903 | − | 1.41469i | |||||
0 | 0 | |||||||||
26851.4 | 0.963815 | 0.481908 | − | 0.876222i | ||||||
0.481908 | + | 0.876222i | ||||||||
0 | 0 | |||||||||
19614.3i | 0.701750i | |||||||||
0 | 0 | |||||||||
−2740.58 | − | 2740.58i | −0.0977327 | − | 0.0977327i | |||||
0 | 0 | |||||||||
5924.29 | − | 5924.29i | 0.210583 | − | 0.210583i | |||||
0 | 0 | |||||||||
16957.9 | 0.600830 | |||||||||
0 | 0 | |||||||||
19627.5i | 0.693171i | 0.938018 | + | 0.346585i | ||||||
−0.938018 | + | 0.346585i | ||||||||
0 | 0 | |||||||||
−4484.26 | − | 4887.08i | −0.157858 | − | 0.172038i | |||||
0 | 0 | |||||||||
44954.6 | + | 44954.6i | 1.57744 | + | 1.57744i | |||||
0 | 0 | |||||||||
−18906.4 | −0.661290 | |||||||||
0 | 0 | |||||||||
−4230.42 | −0.147494 | −0.0737469 | − | 0.997277i | ||||||
−0.0737469 | + | 0.997277i | ||||||||
0 | 0 | |||||||||
−43072.2 | + | 43072.2i | −1.49692 | + | 1.49692i | |||||
0 | 0 | |||||||||
3133.94 | + | 3133.94i | 0.108569 | + | 0.108569i | 0.759305 | − | 0.650735i | ||
−0.650735 | + | 0.759305i | ||||||||
0 | 0 | |||||||||
−15349.0 | −0.530045 | |||||||||
0 | 0 | |||||||||
−2094.44 | + | 2006.35i | −0.0720974 | + | 0.0690650i | |||||
0 | 0 | |||||||||
−273.354 | − | 273.354i | −0.00937997 | − | 0.00937997i | 0.702401 | − | 0.711781i | ||
−0.711781 | + | 0.702401i | ||||||||
0 | 0 | |||||||||
−4468.65 | − | 4468.65i | −0.152854 | − | 0.152854i | |||||
0 | 0 | |||||||||
16959.9i | 0.578298i | |||||||||
0 | 0 | |||||||||
− | 20906.0i | − | 0.710610i | −0.934750 | − | 0.355305i | ||||
0.934750 | − | 0.355305i | ||||||||
0 | 0 | |||||||||
−4223.44 | − | 4223.44i | −0.143107 | − | 0.143107i | |||||
0 | 0 | |||||||||
28438.7 | + | 28438.7i | 0.960599 | + | 0.960599i | |||||
0 | 0 | |||||||||
28942.5 | + | 30213.3i | 0.974559 | + | 1.01735i | |||||
0 | 0 | |||||||||
27364.8 | 0.918558 | |||||||||
0 | 0 | |||||||||
−13840.3 | − | 13840.3i | −0.463133 | − | 0.463133i | |||||
0 | 0 | |||||||||
2338.18 | − | 2338.18i | 0.0779986 | − | 0.0779986i | |||||
0 | 0 | |||||||||
−9771.57 | −0.324956 | −0.162478 | − | 0.986712i | ||||||
−0.162478 | + | 0.986712i | ||||||||
0 | 0 | |||||||||
17540.3 | 0.581501 | |||||||||
0 | 0 | |||||||||
−9977.45 | − | 9977.45i | −0.329754 | − | 0.329754i | 0.522739 | − | 0.852493i | ||
−0.852493 | + | 0.522739i | ||||||||
0 | 0 | |||||||||
−56189.5 | − | 1207.06i | −1.85134 | − | 0.0397705i | |||||
0 | 0 | |||||||||
− | 8196.74i | − | 0.269237i | |||||||
0 | 0 | |||||||||
15291.4 | 0.500732 | 0.250366 | − | 0.968151i | ||||||
0.250366 | + | 0.968151i | ||||||||
0 | 0 | |||||||||
21879.1 | − | 21879.1i | 0.714258 | − | 0.714258i | |||||
0 | 0 | |||||||||
21623.4 | + | 21623.4i | 0.703753 | + | 0.703753i | |||||
0 | 0 | |||||||||
− | 14778.2i | − | 0.479504i | −0.970834 | − | 0.239752i | ||||
0.970834 | − | 0.239752i | ||||||||
0 | 0 | |||||||||
3427.50 | 0.110872 | |||||||||
0 | 0 | |||||||||
456.147 | − | 21233.9i | 0.0147106 | − | 0.684785i | |||||
0 | 0 | |||||||||
−9794.60 | + | 9794.60i | −0.314914 | + | 0.314914i | |||||
0 | 0 | |||||||||
− | 7672.15i | − | 0.245927i | −0.992411 | − | 0.122964i | ||||
0.992411 | − | 0.122964i | ||||||||
0 | 0 | |||||||||
45382.9i | 1.45033i | |||||||||
0 | 0 | |||||||||
−4430.79 | − | 4430.79i | −0.141171 | − | 0.141171i | |||||
0 | 0 | |||||||||
−28731.6 | + | 28731.6i | −0.912677 | + | 0.912677i | −0.996482 | − | 0.0838054i | ||
0.0838054 | + | 0.996482i | ||||||||
0 | 0 | |||||||||
− | 3887.68i | − | 0.123124i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 448.4.j.b.335.37 | 88 | ||
4.3 | odd | 2 | 112.4.j.b.27.9 | ✓ | 88 | ||
7.6 | odd | 2 | inner | 448.4.j.b.335.8 | 88 | ||
16.3 | odd | 4 | inner | 448.4.j.b.111.8 | 88 | ||
16.13 | even | 4 | 112.4.j.b.83.10 | yes | 88 | ||
28.27 | even | 2 | 112.4.j.b.27.10 | yes | 88 | ||
112.13 | odd | 4 | 112.4.j.b.83.9 | yes | 88 | ||
112.83 | even | 4 | inner | 448.4.j.b.111.37 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.j.b.27.9 | ✓ | 88 | 4.3 | odd | 2 | ||
112.4.j.b.27.10 | yes | 88 | 28.27 | even | 2 | ||
112.4.j.b.83.9 | yes | 88 | 112.13 | odd | 4 | ||
112.4.j.b.83.10 | yes | 88 | 16.13 | even | 4 | ||
448.4.j.b.111.8 | 88 | 16.3 | odd | 4 | inner | ||
448.4.j.b.111.37 | 88 | 112.83 | even | 4 | inner | ||
448.4.j.b.335.8 | 88 | 7.6 | odd | 2 | inner | ||
448.4.j.b.335.37 | 88 | 1.1 | even | 1 | trivial |