Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1008.q (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 504) |
Sato-Tate group: |
Embedding invariants
Embedding label | 529.2 | ||
Character | 1008.529 | ||
Dual form | 1008.2.q.k.625.2 |
-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 | |||||||||
−1.57901 | − | 0.711841i | −0.911644 | − | 0.410982i | |||||
0 | 0 | |||||||||
−1.92048 | + | 3.32636i | −0.858863 | + | 1.48759i | 0.0141515 | + | 0.999900i | ||
−0.873014 | + | 0.487694i | ||||||||
0 | 0 | |||||||||
2.55336 | − | 0.693065i | 0.965080 | − | 0.261954i | |||||
0 | 0 | |||||||||
1.98656 | + | 2.24801i | 0.662188 | + | 0.749337i | |||||
0 | 0 | |||||||||
0.903316 | + | 1.56459i | 0.272360 | + | 0.471741i | 0.969466 | − | 0.245227i | ||
−0.697106 | + | 0.716968i | ||||||||
0 | 0 | |||||||||
−0.692713 | − | 1.19981i | −0.192124 | − | 0.332769i | 0.753830 | − | 0.657070i | ||
−0.945954 | + | 0.324301i | ||||||||
0 | 0 | |||||||||
5.40030 | − | 3.88530i | 1.39435 | − | 1.00318i | |||||
0 | 0 | |||||||||
−0.833405 | + | 1.44350i | −0.202130 | + | 0.350100i | −0.949215 | − | 0.314629i | ||
0.747084 | + | 0.664729i | ||||||||
0 | 0 | |||||||||
0.0802084 | + | 0.138925i | 0.0184011 | + | 0.0318716i | 0.875079 | − | 0.483980i | ||
−0.856678 | + | 0.515851i | ||||||||
0 | 0 | |||||||||
−4.52515 | − | 0.723229i | −0.987468 | − | 0.157822i | |||||
0 | 0 | |||||||||
1.60019 | − | 2.77161i | 0.333663 | − | 0.577921i | −0.649564 | − | 0.760307i | ||
0.983227 | + | 0.182386i | ||||||||
0 | 0 | |||||||||
−4.87646 | − | 8.44627i | −0.975291 | − | 1.68925i | |||||
0 | 0 | |||||||||
−1.53658 | − | 4.96376i | −0.295716 | − | 0.955276i | |||||
0 | 0 | |||||||||
−3.78000 | + | 6.54716i | −0.701929 | + | 1.21578i | 0.265859 | + | 0.964012i | ||
−0.967788 | + | 0.251765i | ||||||||
0 | 0 | |||||||||
−3.22021 | −0.578367 | −0.289184 | − | 0.957274i | ||||||
−0.289184 | + | 0.957274i | ||||||||
0 | 0 | |||||||||
−0.312609 | − | 3.11352i | −0.0544182 | − | 0.541995i | |||||
0 | 0 | |||||||||
−2.59829 | + | 9.82442i | −0.439190 | + | 1.66063i | |||||
0 | 0 | |||||||||
1.58395 | + | 2.74348i | 0.260399 | + | 0.451025i | 0.966348 | − | 0.257238i | ||
−0.705949 | + | 0.708263i | ||||||||
0 | 0 | |||||||||
0.239726 | + | 2.38762i | 0.0383869 | + | 0.382326i | |||||
0 | 0 | |||||||||
6.00329 | + | 10.3980i | 0.937556 | + | 1.62389i | 0.770011 | + | 0.638030i | ||
0.167545 | + | 0.985864i | ||||||||
0 | 0 | |||||||||
−3.45480 | + | 5.98389i | −0.526852 | + | 0.912535i | 0.472658 | + | 0.881246i | ||
−0.999510 | + | 0.0312891i | ||||||||
0 | 0 | |||||||||
−11.2929 | + | 2.29078i | −1.68344 | + | 0.341489i | |||||
0 | 0 | |||||||||
−11.4384 | −1.66846 | −0.834232 | − | 0.551414i | ||||||
−0.834232 | + | 0.551414i | ||||||||
0 | 0 | |||||||||
6.03932 | − | 3.53929i | 0.862760 | − | 0.505613i | |||||
0 | 0 | |||||||||
2.34350 | − | 1.68605i | 0.328156 | − | 0.236095i | |||||
0 | 0 | |||||||||
1.37450 | − | 2.38071i | 0.188802 | − | 0.327015i | −0.756049 | − | 0.654515i | ||
0.944851 | + | 0.327500i | ||||||||
0 | 0 | |||||||||
−6.93918 | −0.935679 | |||||||||
0 | 0 | |||||||||
−0.0277576 | − | 0.276460i | −0.00367658 | − | 0.0366180i | |||||
0 | 0 | |||||||||
−15.0705 | −1.96202 | −0.981009 | − | 0.193964i | ||||||
−0.981009 | + | 0.193964i | ||||||||
0 | 0 | |||||||||
−9.20285 | −1.17830 | −0.589152 | − | 0.808022i | ||||||
−0.589152 | + | 0.808022i | ||||||||
0 | 0 | |||||||||
6.63044 | + | 4.36317i | 0.835357 | + | 0.549708i | |||||
0 | 0 | |||||||||
5.32136 | 0.660033 | |||||||||
0 | 0 | |||||||||
12.3366 | 1.50716 | 0.753578 | − | 0.657359i | ||||||
0.753578 | + | 0.657359i | ||||||||
0 | 0 | |||||||||
−4.49967 | + | 3.23733i | −0.541697 | + | 0.389729i | |||||
0 | 0 | |||||||||
6.93289 | 0.822783 | 0.411391 | − | 0.911459i | ||||||
0.411391 | + | 0.911459i | ||||||||
0 | 0 | |||||||||
−6.22457 | + | 10.7813i | −0.728531 | + | 1.26185i | 0.228973 | + | 0.973433i | ||
−0.957504 | + | 0.288420i | ||||||||
0 | 0 | |||||||||
1.68759 | + | 16.8080i | 0.194866 | + | 1.94082i | |||||
0 | 0 | |||||||||
3.39085 | + | 3.36891i | 0.386424 | + | 0.383922i | |||||
0 | 0 | |||||||||
−16.0743 | −1.80850 | −0.904251 | − | 0.427001i | ||||||
−0.904251 | + | 0.427001i | ||||||||
0 | 0 | |||||||||
−1.10712 | + | 8.93165i | −0.123013 | + | 0.992405i | |||||
0 | 0 | |||||||||
1.45280 | − | 2.51633i | 0.159466 | − | 0.276203i | −0.775210 | − | 0.631703i | ||
0.934676 | + | 0.355500i | ||||||||
0 | 0 | |||||||||
−3.20107 | − | 5.54441i | −0.347205 | − | 0.601376i | |||||
0 | 0 | |||||||||
10.6292 | − | 7.64729i | 1.13957 | − | 0.819875i | |||||
0 | 0 | |||||||||
5.04034 | + | 8.73012i | 0.534275 | + | 0.925391i | 0.999198 | + | 0.0400399i | ||
−0.464923 | + | 0.885351i | ||||||||
0 | 0 | |||||||||
−2.60030 | − | 2.58347i | −0.272585 | − | 0.270821i | |||||
0 | 0 | |||||||||
5.08476 | + | 2.29228i | 0.527265 | + | 0.237698i | |||||
0 | 0 | |||||||||
−0.616153 | −0.0632160 | |||||||||
0 | 0 | |||||||||
4.18830 | − | 7.25435i | 0.425257 | − | 0.736567i | −0.571187 | − | 0.820820i | ||
0.996444 | + | 0.0842527i | ||||||||
0 | 0 | |||||||||
−1.72272 | + | 5.13882i | −0.173140 | + | 0.516471i | |||||
0 | 0 | |||||||||
−4.05750 | − | 7.02780i | −0.403736 | − | 0.699292i | 0.590437 | − | 0.807084i | ||
−0.994173 | + | 0.107792i | ||||||||
0 | 0 | |||||||||
−3.76891 | + | 6.52794i | −0.371362 | + | 0.643217i | −0.989775 | − | 0.142635i | ||
0.618414 | + | 0.785853i | ||||||||
0 | 0 | |||||||||
11.0962 | − | 13.6633i | 1.08287 | − | 1.33340i | |||||
0 | 0 | |||||||||
2.95731 | + | 5.12221i | 0.285894 | + | 0.495183i | 0.972826 | − | 0.231539i | ||
−0.686932 | + | 0.726722i | ||||||||
0 | 0 | |||||||||
−4.48409 | + | 7.76668i | −0.429498 | + | 0.743913i | −0.996829 | − | 0.0795776i | ||
0.567331 | + | 0.823490i | ||||||||
0 | 0 | |||||||||
−0.548154 | − | 5.45951i | −0.0520285 | − | 0.518193i | |||||
0 | 0 | |||||||||
−7.98131 | − | 13.8240i | −0.750819 | − | 1.30046i | −0.947426 | − | 0.319974i | ||
0.196608 | − | 0.980482i | ||||||||
0 | 0 | |||||||||
6.14626 | + | 10.6456i | 0.573142 | + | 0.992710i | |||||
0 | 0 | |||||||||
1.32108 | − | 3.94074i | 0.122134 | − | 0.364321i | |||||
0 | 0 | |||||||||
−1.12755 | + | 4.26338i | −0.103362 | + | 0.390824i | |||||
0 | 0 | |||||||||
3.86804 | − | 6.69964i | 0.351640 | − | 0.609059i | |||||
0 | 0 | |||||||||
−2.07755 | − | 20.6920i | −0.187326 | − | 1.86573i | |||||
0 | 0 | |||||||||
18.2557 | 1.63284 | |||||||||
0 | 0 | |||||||||
−8.60913 | −0.763937 | −0.381968 | − | 0.924175i | ||||||
−0.381968 | + | 0.924175i | ||||||||
0 | 0 | |||||||||
9.71476 | − | 6.98937i | 0.855337 | − | 0.615380i | |||||
0 | 0 | |||||||||
−0.964831 | + | 1.67114i | −0.0842976 | + | 0.146008i | −0.905092 | − | 0.425216i | ||
0.820794 | + | 0.571224i | ||||||||
0 | 0 | |||||||||
0.301085 | + | 0.299136i | 0.0261074 | + | 0.0259384i | |||||
0 | 0 | |||||||||
19.4622 | + | 4.42154i | 1.67504 | + | 0.380546i | |||||
0 | 0 | |||||||||
1.85442 | + | 3.21195i | 0.158434 | + | 0.274416i | 0.934304 | − | 0.356477i | ||
−0.775870 | + | 0.630893i | ||||||||
0 | 0 | |||||||||
−0.134568 | − | 0.233079i | −0.0114139 | − | 0.0197695i | 0.860262 | − | 0.509852i | ||
−0.871676 | + | 0.490083i | ||||||||
0 | 0 | |||||||||
18.0614 | + | 8.14233i | 1.52104 | + | 0.685708i | |||||
0 | 0 | |||||||||
1.25148 | − | 2.16762i | 0.104654 | − | 0.181266i | |||||
0 | 0 | |||||||||
−14.5188 | − | 25.1473i | −1.20572 | − | 2.08837i | |||||
0 | 0 | |||||||||
−12.0556 | + | 1.28955i | −0.994328 | + | 0.106361i | |||||
0 | 0 | |||||||||
−4.15880 | + | 7.20325i | −0.340702 | + | 0.590113i | −0.984563 | − | 0.175029i | ||
0.643861 | + | 0.765142i | ||||||||
0 | 0 | |||||||||
4.87069 | + | 8.43628i | 0.396371 | + | 0.686535i | 0.993275 | − | 0.115778i | ||
−0.596904 | + | 0.802313i | ||||||||
0 | 0 | |||||||||
−4.90062 | + | 0.994101i | −0.396192 | + | 0.0803683i | |||||
0 | 0 | |||||||||
6.18434 | − | 10.7116i | 0.496738 | − | 0.860376i | |||||
0 | 0 | |||||||||
24.2580 | 1.93600 | 0.968001 | − | 0.250947i | ||||||
0.968001 | + | 0.250947i | ||||||||
0 | 0 | |||||||||
−3.86504 | + | 2.78074i | −0.306518 | + | 0.220527i | |||||
0 | 0 | |||||||||
2.16496 | − | 8.18597i | 0.170623 | − | 0.645145i | |||||
0 | 0 | |||||||||
−3.91401 | − | 6.77927i | −0.306569 | − | 0.530993i | 0.671040 | − | 0.741421i | ||
−0.977609 | + | 0.210428i | ||||||||
0 | 0 | |||||||||
10.9571 | + | 4.93960i | 0.853006 | + | 0.384547i | |||||
0 | 0 | |||||||||
2.15395 | + | 3.73076i | 0.166678 | + | 0.288695i | 0.937250 | − | 0.348658i | ||
−0.770572 | + | 0.637353i | ||||||||
0 | 0 | |||||||||
5.54030 | − | 9.59608i | 0.426177 | − | 0.738160i | |||||
0 | 0 | |||||||||
−0.152966 | + | 0.456293i | −0.0116976 | + | 0.0348936i | |||||
0 | 0 | |||||||||
−17.3359 | −1.31803 | −0.659014 | − | 0.752131i | ||||||
−0.659014 | + | 0.752131i | ||||||||
0 | 0 | |||||||||
−18.3052 | − | 18.1867i | −1.38374 | − | 1.37478i | |||||
0 | 0 | |||||||||
23.7966 | + | 10.7278i | 1.78866 | + | 0.806353i | |||||
0 | 0 | |||||||||
9.68644 | − | 16.7774i | 0.723998 | − | 1.25400i | −0.235387 | − | 0.971902i | ||
0.959385 | − | 0.282100i | ||||||||
0 | 0 | |||||||||
2.89036 | 0.214839 | 0.107420 | − | 0.994214i | ||||||
0.107420 | + | 0.994214i | ||||||||
0 | 0 | |||||||||
14.5314 | + | 6.55097i | 1.07419 | + | 0.484261i | |||||
0 | 0 | |||||||||
−12.1677 | −0.894590 | |||||||||
0 | 0 | |||||||||
−3.01131 | −0.220209 | |||||||||
0 | 0 | |||||||||
−7.36367 | − | 11.6093i | −0.535628 | − | 0.844454i | |||||
0 | 0 | |||||||||
−3.70044 | −0.267755 | −0.133877 | − | 0.990998i | ||||||
−0.133877 | + | 0.990998i | ||||||||
0 | 0 | |||||||||
−12.7670 | −0.918991 | −0.459495 | − | 0.888180i | ||||||
−0.459495 | + | 0.888180i | ||||||||
0 | 0 | |||||||||
−8.40249 | − | 3.78796i | −0.601715 | − | 0.271261i | |||||
0 | 0 | |||||||||
2.44715 | 0.174352 | 0.0871762 | − | 0.996193i | ||||||
0.0871762 | + | 0.996193i | ||||||||
0 | 0 | |||||||||
−2.24829 | + | 3.89415i | −0.159377 | + | 0.276049i | −0.934644 | − | 0.355584i | ||
0.775267 | + | 0.631633i | ||||||||
0 | 0 | |||||||||
−19.4797 | − | 8.78170i | −1.37399 | − | 0.619413i | |||||
0 | 0 | |||||||||
−5.11411 | + | 19.3371i | −0.358940 | + | 1.35720i | |||||
0 | 0 | |||||||||
−46.1167 | −3.22093 | |||||||||
0 | 0 | |||||||||
9.40950 | − | 1.90874i | 0.654006 | − | 0.132666i | |||||
0 | 0 | |||||||||
−0.144907 | + | 0.250986i | −0.0100234 | + | 0.0173611i | |||||
0 | 0 | |||||||||
−1.09087 | − | 1.88945i | −0.0750987 | − | 0.130075i | 0.826030 | − | 0.563625i | ||
−0.901129 | + | 0.433551i | ||||||||
0 | 0 | |||||||||
−10.9471 | − | 4.93512i | −0.750085 | − | 0.338149i | |||||
0 | 0 | |||||||||
−13.2697 | − | 22.9838i | −0.904988 | − | 1.56749i | |||||
0 | 0 | |||||||||
−8.22237 | + | 2.23182i | −0.558171 | + | 0.151506i | |||||
0 | 0 | |||||||||
17.5032 | − | 12.5929i | 1.18276 | − | 0.850947i | |||||
0 | 0 | |||||||||
2.30924 | 0.155336 | |||||||||
0 | 0 | |||||||||
2.87967 | − | 4.98773i | 0.192837 | − | 0.334003i | −0.753352 | − | 0.657617i | ||
0.946189 | + | 0.323614i | ||||||||
0 | 0 | |||||||||
9.29992 | − | 27.7414i | 0.619995 | − | 1.84943i | |||||
0 | 0 | |||||||||
8.29135 | + | 14.3610i | 0.550316 | + | 0.953175i | 0.998252 | + | 0.0591094i | ||
−0.447935 | + | 0.894066i | ||||||||
0 | 0 | |||||||||
7.29688 | − | 12.6386i | 0.482191 | − | 0.835180i | −0.517600 | − | 0.855623i | ||
0.999791 | + | 0.0204432i | ||||||||
0 | 0 | |||||||||
−2.95608 | − | 7.73329i | −0.194496 | − | 0.508813i | |||||
0 | 0 | |||||||||
0.949438 | + | 1.64448i | 0.0621998 | + | 0.107733i | 0.895448 | − | 0.445165i | ||
−0.833249 | + | 0.552898i | ||||||||
0 | 0 | |||||||||
21.9672 | − | 38.0483i | 1.43298 | − | 2.48200i | |||||
0 | 0 | |||||||||
25.3816 | + | 11.4424i | 1.64871 | + | 0.743261i | |||||
0 | 0 | |||||||||
4.46351 | + | 7.73103i | 0.288721 | + | 0.500079i | 0.973505 | − | 0.228667i | ||
−0.684784 | + | 0.728746i | ||||||||
0 | 0 | |||||||||
12.1465 | + | 21.0383i | 0.782423 | + | 1.35520i | 0.930527 | + | 0.366224i | ||
−0.148104 | + | 0.988972i | ||||||||
0 | 0 | |||||||||
8.10607 | − | 13.3151i | 0.520005 | − | 0.854164i | |||||
0 | 0 | |||||||||
0.174600 | + | 26.8861i | 0.0111548 | + | 1.71769i | |||||
0 | 0 | |||||||||
0.111123 | − | 0.192470i | 0.00707057 | − | 0.0122466i | |||||
0 | 0 | |||||||||
−4.08522 | + | 2.93915i | −0.258890 | + | 0.186261i | |||||
0 | 0 | |||||||||
5.64873 | 0.356545 | 0.178272 | − | 0.983981i | ||||||
0.178272 | + | 0.983981i | ||||||||
0 | 0 | |||||||||
5.78191 | 0.363506 | |||||||||
0 | 0 | |||||||||
1.10779 | + | 11.0334i | 0.0693724 | + | 0.690935i | |||||
0 | 0 | |||||||||
11.7856 | − | 20.4132i | 0.735163 | − | 1.27334i | −0.219489 | − | 0.975615i | ||
0.954652 | − | 0.297724i | ||||||||
0 | 0 | |||||||||
5.94580 | + | 5.90731i | 0.369454 | + | 0.367063i | |||||
0 | 0 | |||||||||
−22.2273 | + | 4.50886i | −1.37584 | + | 0.279091i | |||||
0 | 0 | |||||||||
12.8203 | + | 22.2053i | 0.790531 | + | 1.36924i | 0.925639 | + | 0.378409i | ||
−0.135108 | + | 0.990831i | ||||||||
0 | 0 | |||||||||
5.27940 | + | 9.14419i | 0.324311 | + | 0.561723i | |||||
0 | 0 | |||||||||
−1.74430 | − | 17.3729i | −0.106749 | − | 1.06320i | |||||
0 | 0 | |||||||||
−8.27239 | + | 14.3282i | −0.504376 | + | 0.873606i | 0.495611 | + | 0.868545i | ||
−0.999987 | + | 0.00506090i | ||||||||
0 | 0 | |||||||||
−8.90748 | − | 15.4282i | −0.541091 | − | 0.937197i | −0.998842 | − | 0.0481166i | ||
0.457751 | − | 0.889081i | ||||||||
0 | 0 | |||||||||
2.26689 | + | 5.93032i | 0.137198 | + | 0.358920i | |||||
0 | 0 | |||||||||
8.80996 | − | 15.2593i | 0.531260 | − | 0.920170i | |||||
0 | 0 | |||||||||
2.92191 | + | 5.06089i | 0.175560 | + | 0.304080i | 0.940355 | − | 0.340194i | ||
−0.764795 | + | 0.644274i | ||||||||
0 | 0 | |||||||||
−6.39716 | − | 7.23908i | −0.382988 | − | 0.433392i | |||||
0 | 0 | |||||||||
−10.5591 | + | 18.2889i | −0.629905 | + | 1.09103i | 0.357666 | + | 0.933850i | ||
−0.987570 | + | 0.157177i | ||||||||
0 | 0 | |||||||||
12.7762 | 0.759468 | 0.379734 | − | 0.925096i | ||||||
0.379734 | + | 0.925096i | ||||||||
0 | 0 | |||||||||
0.972914 | + | 0.438603i | 0.0576304 | + | 0.0259806i | |||||
0 | 0 | |||||||||
22.5351 | + | 22.3892i | 1.33020 | + | 1.32159i | |||||
0 | 0 | |||||||||
7.11087 | + | 12.3164i | 0.418287 | + | 0.724494i | |||||
0 | 0 | |||||||||
−11.7773 | + | 8.47330i | −0.690399 | + | 0.496714i | |||||
0 | 0 | |||||||||
5.93828 | + | 10.2854i | 0.346918 | + | 0.600880i | 0.985700 | − | 0.168508i | ||
−0.638782 | + | 0.769388i | ||||||||
0 | 0 | |||||||||
28.9426 | − | 50.1301i | 1.68510 | − | 2.91869i | |||||
0 | 0 | |||||||||
6.37822 | − | 6.88796i | 0.370102 | − | 0.399680i | |||||
0 | 0 | |||||||||
−4.43389 | −0.256419 | |||||||||
0 | 0 | |||||||||
−4.67413 | + | 17.6734i | −0.269413 | + | 1.01868i | |||||
0 | 0 | |||||||||
1.40417 | + | 13.9853i | 0.0806676 | + | 0.803433i | |||||
0 | 0 | |||||||||
17.6739 | − | 30.6120i | 1.01200 | − | 1.75284i | |||||
0 | 0 | |||||||||
3.93298 | 0.224467 | 0.112234 | − | 0.993682i | ||||||
0.112234 | + | 0.993682i | ||||||||
0 | 0 | |||||||||
10.5980 | − | 7.62484i | 0.602900 | − | 0.433762i | |||||
0 | 0 | |||||||||
−1.98221 | −0.112401 | −0.0562005 | − | 0.998420i | ||||||
−0.0562005 | + | 0.998420i | ||||||||
0 | 0 | |||||||||
20.4995 | 1.15870 | 0.579349 | − | 0.815080i | ||||||
0.579349 | + | 0.815080i | ||||||||
0 | 0 | |||||||||
−27.2471 | + | 13.6759i | −1.53520 | + | 0.770548i | |||||
0 | 0 | |||||||||
9.51416 | 0.534369 | 0.267184 | − | 0.963645i | ||||||
0.267184 | + | 0.963645i | ||||||||
0 | 0 | |||||||||
−13.6581 | −0.764709 | |||||||||
0 | 0 | |||||||||
−1.02343 | − | 10.1932i | −0.0571224 | − | 0.568927i | |||||
0 | 0 | |||||||||
−0.267384 | −0.0148777 | |||||||||
0 | 0 | |||||||||
−6.75597 | + | 11.7017i | −0.374754 | + | 0.649093i | |||||
0 | 0 | |||||||||
12.6091 | − | 9.07172i | 0.697284 | − | 0.501667i | |||||
0 | 0 | |||||||||
−29.2064 | + | 7.92756i | −1.61020 | + | 0.437061i | |||||
0 | 0 | |||||||||
−1.52986 | −0.0840886 | −0.0420443 | − | 0.999116i | ||||||
−0.0420443 | + | 0.999116i | ||||||||
0 | 0 | |||||||||
−3.02076 | + | 9.01083i | −0.165536 | + | 0.493790i | |||||
0 | 0 | |||||||||
−23.6921 | + | 41.0360i | −1.29444 | + | 2.24204i | |||||
0 | 0 | |||||||||
10.6972 | + | 18.5281i | 0.582714 | + | 1.00929i | 0.995156 | + | 0.0983063i | ||
−0.412442 | + | 0.910984i | ||||||||
0 | 0 | |||||||||
2.76208 | + | 27.5098i | 0.150016 | + | 1.49413i | |||||
0 | 0 | |||||||||
−2.90887 | − | 5.03831i | −0.157524 | − | 0.272840i | |||||
0 | 0 | |||||||||
12.9676 | − | 13.2227i | 0.700185 | − | 0.713961i | |||||
0 | 0 | |||||||||
−2.12703 | − | 21.1848i | −0.114515 | − | 1.14055i | |||||
0 | 0 | |||||||||
−5.14381 | −0.276134 | −0.138067 | − | 0.990423i | ||||||
−0.138067 | + | 0.990423i | ||||||||
0 | 0 | |||||||||
0.207526 | − | 0.359446i | 0.0111086 | − | 0.0192407i | −0.860418 | − | 0.509590i | ||
0.871526 | + | 0.490349i | ||||||||
0 | 0 | |||||||||
−4.89118 | + | 5.28208i | −0.261072 | + | 0.281936i | |||||
0 | 0 | |||||||||
6.04122 | + | 10.4637i | 0.321542 | + | 0.556926i | 0.980806 | − | 0.194985i | ||
−0.659265 | + | 0.751911i | ||||||||
0 | 0 | |||||||||
−13.3145 | + | 23.0613i | −0.706658 | + | 1.22397i | |||||
0 | 0 | |||||||||
4.81526 | − | 5.92930i | 0.254851 | − | 0.313812i | |||||
0 | 0 | |||||||||
8.14926 | + | 14.1149i | 0.430102 | + | 0.744958i | 0.996882 | − | 0.0789113i | ||
−0.566780 | + | 0.823869i | ||||||||
0 | 0 | |||||||||
9.48713 | − | 16.4322i | 0.499323 | − | 0.864852i | |||||
0 | 0 | |||||||||
−10.8768 | + | 7.82540i | −0.570882 | + | 0.410727i | |||||
0 | 0 | |||||||||
−23.9083 | − | 41.4104i | −1.25142 | − | 2.16752i | |||||
0 | 0 | |||||||||
17.3500 | + | 30.0511i | 0.905664 | + | 1.56866i | 0.820024 | + | 0.572330i | ||
0.0856404 | + | 0.996326i | ||||||||
0 | 0 | |||||||||
−11.4489 | + | 34.1518i | −0.596007 | + | 1.77787i | |||||
0 | 0 | |||||||||
1.85962 | − | 7.03143i | 0.0965465 | − | 0.365054i | |||||
0 | 0 | |||||||||
7.75329 | − | 13.4291i | 0.401450 | − | 0.695332i | −0.592451 | − | 0.805606i | ||
0.993901 | + | 0.110274i | ||||||||
0 | 0 | |||||||||
−28.8260 | − | 12.9952i | −1.48857 | − | 0.671067i | |||||
0 | 0 | |||||||||
10.4738 | 0.539430 | |||||||||
0 | 0 | |||||||||
16.1820 | 0.831214 | 0.415607 | − | 0.909544i | ||||||
0.415607 | + | 0.909544i | ||||||||
0 | 0 | |||||||||
13.5939 | + | 6.12833i | 0.696438 | + | 0.313964i | |||||
0 | 0 | |||||||||
2.17027 | − | 3.75902i | 0.110896 | − | 0.192077i | −0.805236 | − | 0.592955i | ||
0.916132 | + | 0.400877i | ||||||||
0 | 0 | |||||||||
−17.7183 | + | 4.80931i | −0.903006 | + | 0.245105i | |||||
0 | 0 | |||||||||
−20.3151 | + | 4.12095i | −1.03267 | + | 0.209480i | |||||
0 | 0 | |||||||||
−12.7731 | − | 22.1237i | −0.647624 | − | 1.12172i | −0.983689 | − | 0.179879i | ||
0.336065 | − | 0.941839i | ||||||||
0 | 0 | |||||||||
2.66722 | + | 4.61975i | 0.134887 | + | 0.233631i | |||||
0 | 0 | |||||||||
2.71306 | − | 1.95194i | 0.136856 | − | 0.0984623i | |||||
0 | 0 | |||||||||
30.8703 | − | 53.4690i | 1.55326 | − | 2.69032i | |||||
0 | 0 | |||||||||
2.28225 | + | 3.95297i | 0.114543 | + | 0.198394i | 0.917597 | − | 0.397512i | ||
−0.803054 | + | 0.595906i | ||||||||
0 | 0 | |||||||||
−0.262480 | − | 0.686665i | −0.0131404 | − | 0.0343762i | |||||
0 | 0 | |||||||||
−0.668128 | + | 1.15723i | −0.0333647 | + | 0.0577894i | −0.882226 | − | 0.470827i | ||
0.848861 | + | 0.528616i | ||||||||
0 | 0 | |||||||||
2.23068 | + | 3.86366i | 0.111118 | + | 0.192463i | |||||
0 | 0 | |||||||||
−27.5837 | − | 20.8357i | −1.37064 | − | 1.03533i | |||||
0 | 0 | |||||||||
−2.86161 | + | 4.95645i | −0.141845 | + | 0.245682i | |||||
0 | 0 | |||||||||
20.6664 | 1.02189 | 0.510944 | − | 0.859614i | ||||||
0.510944 | + | 0.859614i | ||||||||
0 | 0 | |||||||||
−0.641757 | − | 6.39177i | −0.0316555 | − | 0.315283i | |||||
0 | 0 | |||||||||
−38.4806 | + | 10.4449i | −1.89350 | + | 0.513958i | |||||
0 | 0 | |||||||||
5.58015 | + | 9.66510i | 0.273919 | + | 0.474441i | |||||
0 | 0 | |||||||||
0.0465699 | + | 0.463826i | 0.00228054 | + | 0.0227137i | |||||
0 | 0 | |||||||||
−10.5227 | − | 18.2259i | −0.514069 | − | 0.890394i | −0.999867 | − | 0.0163228i | ||
0.485797 | − | 0.874071i | ||||||||
0 | 0 | |||||||||
−8.51630 | + | 14.7507i | −0.415059 | + | 0.718903i | −0.995435 | − | 0.0954456i | ||
0.580376 | + | 0.814349i | ||||||||
0 | 0 | |||||||||
−22.7231 | − | 25.7137i | −1.10484 | − | 1.25024i | |||||
0 | 0 | |||||||||
16.2563 | 0.788544 | |||||||||
0 | 0 | |||||||||
−23.4982 | + | 6.37818i | −1.13716 | + | 0.308662i | |||||
0 | 0 | |||||||||
−3.51910 | + | 2.53185i | −0.169904 | + | 0.122239i | |||||
0 | 0 | |||||||||
−18.2925 | + | 31.6836i | −0.881121 | + | 1.52615i | −0.0310244 | + | 0.999519i | ||
−0.850096 | + | 0.526627i | ||||||||
0 | 0 | |||||||||
−23.6571 | −1.13689 | −0.568444 | − | 0.822722i | ||||||
−0.568444 | + | 0.822722i | ||||||||
0 | 0 | |||||||||
5.02450 | + | 50.0430i | 0.240906 | + | 2.39938i | |||||
0 | 0 | |||||||||
0.513395 | 0.0245590 | |||||||||
0 | 0 | |||||||||
−20.7864 | −0.992082 | −0.496041 | − | 0.868299i | ||||||
−0.496041 | + | 0.868299i | ||||||||
0 | 0 | |||||||||
19.9539 | + | 6.54543i | 0.950185 | + | 0.311687i | |||||
0 | 0 | |||||||||
−7.42807 | −0.352918 | −0.176459 | − | 0.984308i | ||||||
−0.176459 | + | 0.984308i | ||||||||
0 | 0 | |||||||||
−38.7194 | −1.83547 | |||||||||
0 | 0 | |||||||||
11.6944 | − | 8.41363i | 0.553125 | − | 0.397951i | |||||
0 | 0 | |||||||||
−8.15800 | −0.385000 | −0.192500 | − | 0.981297i | ||||||
−0.192500 | + | 0.981297i | ||||||||
0 | 0 | |||||||||
−10.8457 | + | 18.7854i | −0.510705 | + | 0.884568i | |||||
0 | 0 | |||||||||
−1.68559 | − | 16.7882i | −0.0791960 | − | 0.788776i | |||||
0 | 0 | |||||||||
13.5873 | − | 3.68805i | 0.636985 | − | 0.172898i | |||||
0 | 0 | |||||||||
14.3058 | 0.669199 | 0.334600 | − | 0.942360i | ||||||
0.334600 | + | 0.942360i | ||||||||
0 | 0 | |||||||||
8.44578 | + | 1.91876i | 0.394215 | + | 0.0895602i | |||||
0 | 0 | |||||||||
7.71961 | − | 13.3708i | 0.359538 | − | 0.622738i | −0.628346 | − | 0.777934i | ||
0.987884 | + | 0.155196i | ||||||||
0 | 0 | |||||||||
−10.5531 | − | 18.2785i | −0.490444 | − | 0.849474i | 0.509496 | − | 0.860473i | ||
−0.999940 | + | 0.0109995i | ||||||||
0 | 0 | |||||||||
−17.3901 | + | 12.5115i | −0.806447 | + | 0.580206i | |||||
0 | 0 | |||||||||
−3.49896 | − | 6.06037i | −0.161912 | − | 0.280440i | 0.773642 | − | 0.633623i | ||
−0.935555 | + | 0.353182i | ||||||||
0 | 0 | |||||||||
31.4998 | − | 8.55007i | 1.45453 | − | 0.394805i | |||||
0 | 0 | |||||||||
−38.3037 | − | 17.2679i | −1.76494 | − | 0.795661i | |||||
0 | 0 | |||||||||
−12.4831 | −0.573974 | |||||||||
0 | 0 | |||||||||
0.782265 | − | 1.35492i | 0.0358928 | − | 0.0621681i | |||||
0 | 0 | |||||||||
8.08240 | − | 1.63953i | 0.370068 | − | 0.0750691i | |||||
0 | 0 | |||||||||
1.54406 | + | 2.67440i | 0.0705500 | + | 0.122196i | 0.899142 | − | 0.437656i | ||
−0.828592 | + | 0.559852i | ||||||||
0 | 0 | |||||||||
2.19444 | − | 3.80089i | 0.100058 | − | 0.173305i | |||||
0 | 0 | |||||||||
−9.24561 | + | 11.3846i | −0.420690 | + | 0.518019i | |||||
0 | 0 | |||||||||
16.0871 | + | 27.8636i | 0.730475 | + | 1.26522i | |||||
0 | 0 | |||||||||
−4.90011 | + | 8.48725i | −0.222045 | + | 0.384594i | −0.955429 | − | 0.295221i | ||
0.733384 | + | 0.679815i | ||||||||
0 | 0 | |||||||||
1.35452 | + | 13.4907i | 0.0612533 | + | 0.610071i | |||||
0 | 0 | |||||||||
−9.98641 | − | 17.2970i | −0.450680 | − | 0.780601i | 0.547748 | − | 0.836643i | ||
−0.998428 | + | 0.0560419i | ||||||||
0 | 0 | |||||||||
−6.30055 | − | 10.9129i | −0.283762 | − | 0.491491i | |||||
0 | 0 | |||||||||
−13.7851 | − | 15.5994i | −0.619596 | − | 0.701140i | |||||
0 | 0 | |||||||||
17.7022 | − | 4.80495i | 0.794052 | − | 0.215531i | |||||
0 | 0 | |||||||||
−10.1650 | + | 17.6062i | −0.455046 | + | 0.788163i | −0.998691 | − | 0.0511526i | ||
0.543645 | + | 0.839315i | ||||||||
0 | 0 | |||||||||
−0.745415 | − | 7.42419i | −0.0333027 | − | 0.331688i | |||||
0 | 0 | |||||||||
23.9595 | 1.06830 | 0.534151 | − | 0.845389i | ||||||
0.534151 | + | 0.845389i | ||||||||
0 | 0 | |||||||||
31.1693 | 1.38702 | |||||||||
0 | 0 | |||||||||
−15.5791 | + | 11.2085i | −0.691891 | + | 0.497788i | |||||
0 | 0 | |||||||||
−5.03046 | + | 8.71302i | −0.222971 | + | 0.386198i | −0.955709 | − | 0.294314i | ||
0.732737 | + | 0.680511i | ||||||||
0 | 0 | |||||||||
−8.42146 | + | 31.8425i | −0.372544 | + | 1.40863i | |||||
0 | 0 | |||||||||
0.566343 | − | 0.611605i | 0.0250047 | − | 0.0270030i | |||||
0 | 0 | |||||||||
−14.4762 | − | 25.0735i | −0.637898 | − | 1.10487i | |||||
0 | 0 | |||||||||
−10.3325 | − | 17.8964i | −0.454423 | − | 0.787083i | |||||
0 | 0 | |||||||||
27.3737 | + | 12.3404i | 1.20157 | + | 0.541685i | |||||
0 | 0 | |||||||||
7.99821 | − | 13.8533i | 0.350408 | − | 0.606924i | −0.635913 | − | 0.771761i | ||
0.986321 | + | 0.164836i | ||||||||
0 | 0 | |||||||||
18.7103 | + | 32.4072i | 0.818146 | + | 1.41707i | 0.907047 | + | 0.421029i | ||
−0.0889016 | + | 0.996040i | ||||||||
0 | 0 | |||||||||
15.9581 | + | 41.7474i | 0.696468 | + | 1.82201i | |||||
0 | 0 | |||||||||
2.68374 | − | 4.64838i | 0.116906 | − | 0.202487i | |||||
0 | 0 | |||||||||
6.37877 | + | 11.0484i | 0.277338 | + | 0.480364i | |||||
0 | 0 | |||||||||
−29.9386 | − | 33.8788i | −1.29922 | − | 1.47021i | |||||
0 | 0 | |||||||||
8.31711 | − | 14.4057i | 0.360254 | − | 0.623978i | |||||
0 | 0 | |||||||||
−22.7178 | −0.982175 | |||||||||
0 | 0 | |||||||||
−27.2379 | + | 19.5965i | −1.17540 | + | 0.845653i | |||||
0 | 0 | |||||||||
10.9930 | + | 6.25195i | 0.473500 | + | 0.269291i | |||||
0 | 0 | |||||||||
0.229159 | + | 0.396916i | 0.00985233 | + | 0.0170647i | 0.870910 | − | 0.491443i | ||
−0.861057 | + | 0.508508i | ||||||||
0 | 0 | |||||||||
−4.56392 | − | 2.05748i | −0.195857 | − | 0.0882949i | |||||
0 | 0 | |||||||||
−17.2232 | − | 29.8314i | −0.737760 | − | 1.27784i | |||||
0 | 0 | |||||||||
11.2013 | − | 19.4011i | 0.478931 | − | 0.829533i | −0.520777 | − | 0.853693i | ||
0.999708 | + | 0.0241596i | ||||||||
0 | 0 | |||||||||
−18.2821 | − | 20.6881i | −0.780259 | − | 0.882948i | |||||
0 | 0 | |||||||||
−1.21275 | −0.0516650 | |||||||||
0 | 0 | |||||||||
−41.0436 | + | 11.1405i | −1.74535 | + | 0.473744i | |||||
0 | 0 | |||||||||
19.2130 | + | 8.66149i | 0.815547 | + | 0.367660i | |||||
0 | 0 | |||||||||
10.4155 | − | 18.0401i | 0.441317 | − | 0.764383i | −0.556471 | − | 0.830867i | ||
0.997787 | + | 0.0664841i | ||||||||
0 | 0 | |||||||||
9.57275 | 0.404884 | |||||||||
0 | 0 | |||||||||
4.75490 | + | 2.14357i | 0.200752 | + | 0.0905018i | |||||
0 | 0 | |||||||||
−8.80605 | −0.371131 | −0.185565 | − | 0.982632i | ||||||
−0.185565 | + | 0.982632i | ||||||||
0 | 0 | |||||||||
61.3117 | 2.57940 | |||||||||
0 | 0 | |||||||||
3.36333 | + | 23.5730i | 0.141247 | + | 0.989974i | |||||
0 | 0 | |||||||||
18.9857 | 0.795923 | 0.397962 | − | 0.917402i | ||||||
0.397962 | + | 0.917402i | ||||||||
0 | 0 | |||||||||
15.7597 | 0.659523 | 0.329762 | − | 0.944064i | ||||||
0.329762 | + | 0.944064i | ||||||||
0 | 0 | |||||||||
5.84305 | + | 2.63413i | 0.244097 | + | 0.110042i | |||||
0 | 0 | |||||||||
−31.2131 | −1.30167 | |||||||||
0 | 0 | |||||||||
−15.9306 | + | 27.5927i | −0.663201 | + | 1.14870i | 0.316569 | + | 0.948570i | ||
−0.979770 | + | 0.200128i | ||||||||
0 | 0 | |||||||||
20.1593 | + | 9.08809i | 0.837792 | + | 0.377688i | |||||
0 | 0 | |||||||||
1.96555 | − | 7.43199i | 0.0815449 | − | 0.308331i | |||||
0 | 0 | |||||||||
4.96644 | 0.205689 | |||||||||
0 | 0 | |||||||||
10.5712 | + | 11.9625i | 0.437066 | + | 0.494587i | |||||
0 | 0 | |||||||||
20.3597 | − | 35.2640i | 0.840333 | − | 1.45550i | −0.0492799 | − | 0.998785i | ||
0.889613 | − | 0.456715i | ||||||||
0 | 0 | |||||||||
−0.258288 | − | 0.447368i | −0.0106426 | − | 0.0184335i | |||||
0 | 0 | |||||||||
−3.86409 | − | 1.74198i | −0.158947 | − | 0.0716557i | |||||
0 | 0 | |||||||||
−14.0693 | − | 24.3688i | −0.577759 | − | 1.00071i | −0.995736 | − | 0.0922500i | ||
0.417977 | − | 0.908458i | ||||||||
0 | 0 | |||||||||
−12.0161 | − | 11.9383i | −0.492613 | − | 0.489425i | |||||
0 | 0 | |||||||||
6.32209 | − | 4.54849i | 0.258746 | − | 0.186157i | |||||
0 | 0 | |||||||||
−32.9926 | −1.34804 | −0.674020 | − | 0.738713i | ||||||
−0.674020 | + | 0.738713i | ||||||||
0 | 0 | |||||||||
−1.98103 | + | 3.43124i | −0.0808079 | + | 0.139963i | −0.903597 | − | 0.428383i | ||
0.822789 | + | 0.568347i | ||||||||
0 | 0 | |||||||||
24.5075 | + | 27.7328i | 0.998021 | + | 1.12937i | |||||
0 | 0 | |||||||||
14.8570 | + | 25.7330i | 0.604021 | + | 1.04620i | |||||
0 | 0 | |||||||||
17.0132 | − | 29.4676i | 0.690543 | − | 1.19605i | −0.281118 | − | 0.959673i | ||
0.971660 | − | 0.236382i | ||||||||
0 | 0 | |||||||||
21.8402 | − | 26.8930i | 0.885008 | − | 1.08976i | |||||
0 | 0 | |||||||||
7.92354 | + | 13.7240i | 0.320552 | + | 0.555212i | |||||
0 | 0 | |||||||||
−15.2967 | + | 26.4946i | −0.617827 | + | 1.07011i | 0.372054 | + | 0.928211i | ||
−0.989881 | + | 0.141897i | ||||||||
0 | 0 | |||||||||
72.8188 | + | 32.8277i | 2.93634 | + | 1.32374i | |||||
0 | 0 | |||||||||
18.7646 | + | 32.5013i | 0.755435 | + | 1.30845i | 0.945158 | + | 0.326614i | ||
−0.189723 | + | 0.981838i | ||||||||
0 | 0 | |||||||||
−2.92302 | − | 5.06282i | −0.117486 | − | 0.203492i | 0.801285 | − | 0.598283i | ||
−0.918771 | + | 0.394791i | ||||||||
0 | 0 | |||||||||
−16.2164 | − | 3.68415i | −0.650744 | − | 0.147840i | |||||
0 | 0 | |||||||||
18.9203 | + | 18.7979i | 0.758028 | + | 0.753121i | |||||
0 | 0 | |||||||||
−10.6774 | + | 18.4937i | −0.427095 | + | 0.739749i | |||||
0 | 0 | |||||||||
0.407472 | − | 0.293160i | 0.0162729 | − | 0.0117077i | |||||
0 | 0 | |||||||||
−5.28028 | −0.210539 | |||||||||
0 | 0 | |||||||||
−25.6347 | −1.02050 | −0.510251 | − | 0.860025i | ||||||
−0.510251 | + | 0.860025i | ||||||||
0 | 0 | |||||||||
0.377516 | + | 3.75999i | 0.0150049 | + | 0.149446i | |||||
0 | 0 | |||||||||
16.5336 | − | 28.6371i | 0.656117 | − | 1.13643i | |||||
0 | 0 | |||||||||
−8.43001 | − | 4.79435i | −0.334009 | − | 0.189959i | |||||
0 | 0 | |||||||||
13.7726 | + | 15.5852i | 0.544837 | + | 0.616542i | |||||
0 | 0 | |||||||||
−12.9824 | − | 22.4861i | −0.512772 | − | 0.888147i | −0.999890 | − | 0.0148113i | ||
0.487118 | − | 0.873336i | ||||||||
0 | 0 | |||||||||
22.5634 | + | 39.0809i | 0.889812 | + | 1.54120i | 0.840097 | + | 0.542436i | ||
0.0497151 | + | 0.998763i | ||||||||
0 | 0 | |||||||||
4.59223 | + | 45.7377i | 0.180819 | + | 1.80092i | |||||
0 | 0 | |||||||||
−2.70324 | + | 4.68215i | −0.106275 | + | 0.184074i | −0.914259 | − | 0.405131i | ||
0.807983 | + | 0.589206i | ||||||||
0 | 0 | |||||||||
−13.6135 | − | 23.5792i | −0.534375 | − | 0.925564i | |||||
0 | 0 | |||||||||
14.5719 | + | 2.32895i | 0.571119 | + | 0.0912788i | |||||
0 | 0 | |||||||||
15.9515 | − | 27.6288i | 0.624231 | − | 1.08120i | −0.364458 | − | 0.931220i | ||
0.988689 | − | 0.149980i | ||||||||
0 | 0 | |||||||||
−3.70587 | − | 6.41875i | −0.144800 | − | 0.250801i | |||||
0 | 0 | |||||||||
−36.6020 | + | 7.42479i | −1.42798 | + | 0.289669i | |||||
0 | 0 | |||||||||
−2.50215 | + | 4.33385i | −0.0974699 | + | 0.168823i | −0.910637 | − | 0.413208i | ||
0.813167 | + | 0.582031i | ||||||||
0 | 0 | |||||||||
9.63406 | 0.374721 | 0.187361 | − | 0.982291i | ||||||
0.187361 | + | 0.982291i | ||||||||
0 | 0 | |||||||||
−3.64632 | − | 1.64381i | −0.141611 | − | 0.0638404i | |||||
0 | 0 | |||||||||
−1.57326 | + | 0.427034i | −0.0610085 | + | 0.0165597i | |||||
0 | 0 | |||||||||
12.0975 | + | 20.9534i | 0.468415 | + | 0.811319i | |||||
0 | 0 | |||||||||
−8.09751 | + | 5.82583i | −0.313068 | + | 0.225240i | |||||
0 | 0 | |||||||||
−8.31308 | − | 14.3987i | −0.320923 | − | 0.555855i | |||||
0 | 0 | |||||||||
13.5885 | − | 23.5359i | 0.523797 | − | 0.907243i | −0.475819 | − | 0.879543i | ||
0.999616 | − | 0.0276998i | ||||||||
0 | 0 | |||||||||
−34.4322 | + | 37.1840i | −1.32529 | + | 1.43121i | |||||
0 | 0 | |||||||||
−38.0502 | −1.46239 | −0.731194 | − | 0.682169i | ||||||
−0.731194 | + | 0.682169i | ||||||||
0 | 0 | |||||||||
5.66651 | − | 21.4257i | 0.217461 | − | 0.822244i | |||||
0 | 0 | |||||||||
−2.86937 | − | 28.5784i | −0.109955 | − | 1.09513i | |||||
0 | 0 | |||||||||
−15.0571 | + | 26.0797i | −0.576146 | + | 0.997913i | 0.419771 | + | 0.907630i | ||
−0.995916 | + | 0.0902831i | ||||||||
0 | 0 | |||||||||
−14.2455 | −0.544293 | |||||||||
0 | 0 | |||||||||
−20.5185 | + | 14.7622i | −0.782830 | + | 0.563215i | |||||
0 | 0 | |||||||||
−3.80854 | −0.145094 | |||||||||
0 | 0 | |||||||||
−14.3902 | −0.547429 | −0.273714 | − | 0.961811i | ||||||
−0.273714 | + | 0.961811i | ||||||||
0 | 0 | |||||||||
−0.837189 | + | 14.3152i | −0.0318022 | + | 0.543791i | |||||
0 | 0 | |||||||||
1.03374 | 0.0392120 | |||||||||
0 | 0 | |||||||||
−20.0127 | −0.758034 | |||||||||
0 | 0 | |||||||||
−0.328571 | − | 3.27250i | −0.0124277 | − | 0.123777i | |||||
0 | 0 | |||||||||
14.4170 | 0.544521 | 0.272261 | − | 0.962224i | ||||||
0.272261 | + | 0.962224i | ||||||||
0 | 0 | |||||||||
−0.254092 | + | 0.440100i | −0.00958325 | + | 0.0165987i | |||||
0 | 0 | |||||||||
−61.7708 | + | 44.4416i | −2.32642 | + | 1.67377i | |||||
0 | 0 | |||||||||
−15.2310 | − | 15.1324i | −0.572820 | − | 0.569113i | |||||
0 | 0 | |||||||||
11.4882 | 0.431448 | 0.215724 | − | 0.976454i | ||||||
0.215724 | + | 0.976454i | ||||||||
0 | 0 | |||||||||
−31.9327 | − | 36.1353i | −1.19757 | − | 1.35518i | |||||
0 | 0 | |||||||||
−5.15296 | + | 8.92519i | −0.192980 | + | 0.334251i | |||||
0 | 0 | |||||||||
4.80686 | + | 8.32573i | 0.179766 | + | 0.311365i | |||||
0 | 0 | |||||||||
−1.54468 | − | 15.3847i | −0.0576871 | − | 0.574552i | |||||
0 | 0 | |||||||||
−17.9451 | − | 31.0818i | −0.669240 | − | 1.15916i | −0.978117 | − | 0.208055i | ||
0.308877 | − | 0.951102i | ||||||||
0 | 0 | |||||||||
−5.09910 | + | 19.2803i | −0.189901 | + | 0.718036i | |||||
0 | 0 | |||||||||
−4.20351 | − | 41.8661i | −0.156330 | − | 1.55702i | |||||
0 | 0 | |||||||||
73.7321 | 2.73834 | |||||||||
0 | 0 | |||||||||
5.03060 | − | 8.71326i | 0.186575 | − | 0.323157i | −0.757531 | − | 0.652799i | ||
0.944106 | + | 0.329642i | ||||||||
0 | 0 | |||||||||
−22.2778 | + | 15.2545i | −0.825104 | + | 0.564980i | |||||
0 | 0 | |||||||||
−5.75850 | − | 9.97401i | −0.212986 | − | 0.368902i | |||||
0 | 0 | |||||||||
−16.5690 | + | 28.6984i | −0.611992 | + | 1.06000i | 0.378913 | + | 0.925432i | ||
−0.990904 | + | 0.134568i | ||||||||
0 | 0 | |||||||||
18.8629 | − | 42.5778i | 0.695770 | − | 1.57051i | |||||
0 | 0 | |||||||||
11.1438 | + | 19.3017i | 0.410489 | + | 0.710987i | |||||
0 | 0 | |||||||||
−21.9237 | + | 37.9729i | −0.806475 | + | 1.39686i | 0.108816 | + | 0.994062i | ||
−0.915291 | + | 0.402793i | ||||||||
0 | 0 | |||||||||
−0.312473 | + | 0.224811i | −0.0114790 | + | 0.00825865i | |||||
0 | 0 | |||||||||
−4.50115 | − | 7.79622i | −0.165131 | − | 0.286016i | 0.771571 | − | 0.636144i | ||
−0.936702 | + | 0.350128i | ||||||||
0 | 0 | |||||||||
−15.9738 | − | 27.6673i | −0.585233 | − | 1.01365i | |||||
0 | 0 | |||||||||
8.54283 | − | 1.73293i | 0.312566 | − | 0.0634046i | |||||
0 | 0 | |||||||||
11.1011 | + | 11.0293i | 0.405626 | + | 0.403000i | |||||
0 | 0 | |||||||||
5.59141 | − | 9.68460i | 0.204033 | − | 0.353396i | −0.745791 | − | 0.666180i | ||
0.949824 | + | 0.312784i | ||||||||
0 | 0 | |||||||||
−8.91942 | − | 4.02100i | −0.325042 | − | 0.146533i | |||||
0 | 0 | |||||||||
−37.4162 | −1.36171 | |||||||||
0 | 0 | |||||||||
42.1431 | 1.53172 | 0.765859 | − | 0.643009i | ||||||
0.765859 | + | 0.643009i | ||||||||
0 | 0 | |||||||||
−9.12971 | − | 4.11580i | −0.331388 | − | 0.149394i | |||||
0 | 0 | |||||||||
−1.14155 | + | 1.97721i | −0.0413810 | + | 0.0716740i | −0.885974 | − | 0.463735i | ||
0.844593 | + | 0.535409i | ||||||||
0 | 0 | |||||||||
−6.06670 | + | 22.9389i | −0.219629 | + | 0.830444i | |||||
0 | 0 | |||||||||
6.10478 | − | 18.2104i | 0.220719 | − | 0.658398i | |||||
0 | 0 | |||||||||
10.4396 | + | 18.0819i | 0.376951 | + | 0.652898i | |||||
0 | 0 | |||||||||
8.96676 | + | 15.5309i | 0.323350 | + | 0.560058i | 0.981177 | − | 0.193111i | ||
−0.657827 | + | 0.753169i | ||||||||
0 | 0 | |||||||||
−33.1405 | + | 23.8432i | −1.19353 | + | 0.858693i | |||||
0 | 0 | |||||||||
17.4807 | − | 30.2775i | 0.628737 | − | 1.08901i | −0.359068 | − | 0.933311i | ||
0.987805 | − | 0.155694i | ||||||||
0 | 0 | |||||||||
15.7032 | + | 27.1988i | 0.564077 | + | 0.977009i | |||||
0 | 0 | |||||||||
−5.18343 | − | 13.5602i | −0.185955 | − | 0.486469i | |||||
0 | 0 | |||||||||
−0.963028 | + | 1.66801i | −0.0345041 | + | 0.0597628i | |||||
0 | 0 | |||||||||
6.26259 | + | 10.8471i | 0.224093 | + | 0.388141i | |||||
0 | 0 | |||||||||
38.3068 | + | 8.70277i | 1.36897 | + | 0.311011i | |||||
0 | 0 | |||||||||
−46.5870 | + | 80.6910i | −1.66276 | + | 2.87998i | |||||
0 | 0 | |||||||||
28.3564 | 1.01079 | 0.505397 | − | 0.862887i | ||||||
0.505397 | + | 0.862887i | ||||||||
0 | 0 | |||||||||
−4.43668 | − | 44.1885i | −0.157950 | − | 1.57315i | |||||
0 | 0 | |||||||||
−29.9601 | − | 29.7662i | −1.06526 | − | 1.05836i | |||||
0 | 0 | |||||||||
6.37494 | + | 11.0417i | 0.226381 | + | 0.392103i | |||||
0 | 0 | |||||||||
−1.82703 | − | 18.1969i | −0.0647982 | − | 0.645377i | |||||
0 | 0 | |||||||||
−9.51922 | − | 16.4878i | −0.337188 | − | 0.584027i | 0.646715 | − | 0.762732i | ||
−0.983903 | + | 0.178705i | ||||||||
0 | 0 | |||||||||
9.53283 | − | 16.5113i | 0.337247 | − | 0.584129i | |||||
0 | 0 | |||||||||
−9.61246 | + | 28.6737i | −0.339640 | + | 1.01313i | |||||
0 | 0 | |||||||||
−22.4910 | −0.793691 | |||||||||
0 | 0 | |||||||||
23.0717 | + | 22.9224i | 0.813172 | + | 0.807908i | |||||
0 | 0 | |||||||||
23.2616 | − | 16.7358i | 0.818847 | − | 0.589128i | |||||
0 | 0 | |||||||||
−10.4529 | + | 18.1050i | −0.367505 | + | 0.636538i | −0.989175 | − | 0.146742i | ||
0.621670 | + | 0.783280i | ||||||||
0 | 0 | |||||||||
−17.5392 | −0.615884 | −0.307942 | − | 0.951405i | ||||||
−0.307942 | + | 0.951405i | ||||||||
0 | 0 | |||||||||
3.08260 | + | 30.7021i | 0.108111 | + | 1.07677i | |||||
0 | 0 | |||||||||
30.0671 | 1.05320 | |||||||||
0 | 0 | |||||||||
−1.10842 | −0.0387786 | |||||||||
0 | 0 | |||||||||
0.642004 | − | 10.9777i | 0.0224334 | − | 0.383593i | |||||
0 | 0 | |||||||||
−34.9762 | −1.22068 | −0.610339 | − | 0.792140i | ||||||
−0.610339 | + | 0.792140i | ||||||||
0 | 0 | |||||||||
30.4235 | 1.06050 | 0.530249 | − | 0.847842i | ||||||
0.530249 | + | 0.847842i | ||||||||
0 | 0 | |||||||||
−24.7732 | + | 17.8233i | −0.862493 | + | 0.620529i | |||||
0 | 0 | |||||||||
25.6276 | 0.891158 | 0.445579 | − | 0.895243i | ||||||
0.445579 | + | 0.895243i | ||||||||
0 | 0 | |||||||||
23.9403 | − | 41.4658i | 0.831481 | − | 1.44017i | −0.0653833 | − | 0.997860i | ||
0.896864 | − | 0.442307i | ||||||||
0 | 0 | |||||||||
−1.01118 | − | 10.0712i | −0.0350775 | − | 0.349364i | |||||
0 | 0 | |||||||||
0.0757689 | + | 11.6674i | 0.00262524 | + | 0.404252i | |||||
0 | 0 | |||||||||
−16.5465 | −0.572614 | |||||||||
0 | 0 | |||||||||
4.94813 | + | 15.9844i | 0.171032 | + | 0.552501i | |||||
0 | 0 | |||||||||
21.8466 | − | 37.8394i | 0.754227 | − | 1.30636i | −0.191530 | − | 0.981487i | ||
0.945758 | − | 0.324873i | ||||||||
0 | 0 | |||||||||
−14.0769 | − | 24.3818i | −0.485409 | − | 0.840753i | |||||
0 | 0 | |||||||||
29.6918 | − | 21.3621i | 1.02264 | − | 0.735749i | |||||
0 | 0 | |||||||||
21.2800 | + | 36.8581i | 0.732055 | + | 1.26796i | |||||
0 | 0 | |||||||||
5.23322 | − | 19.7874i | 0.179816 | − | 0.679904i | |||||
0 | 0 | |||||||||
−20.1738 | − | 9.09464i | −0.692364 | − | 0.312127i | |||||
0 | 0 | |||||||||
10.1385 | 0.347543 | |||||||||
0 | 0 | |||||||||
8.33994 | − | 14.4452i | 0.285554 | − | 0.494594i | −0.687189 | − | 0.726478i | ||
0.972743 | + | 0.231884i | ||||||||
0 | 0 | |||||||||
−1.22403 | − | 1.38512i | −0.0418609 | − | 0.0473701i | |||||
0 | 0 | |||||||||
−7.21452 | − | 12.4959i | −0.246443 | − | 0.426852i | 0.716093 | − | 0.698005i | ||
−0.962536 | + | 0.271152i | ||||||||
0 | 0 | |||||||||
11.3867 | − | 19.7223i | 0.388508 | − | 0.672915i | −0.603741 | − | 0.797180i | ||
0.992249 | + | 0.124265i | ||||||||
0 | 0 | |||||||||
−19.6456 | − | 51.3942i | −0.669521 | − | 1.75151i | |||||
0 | 0 | |||||||||
5.97266 | + | 10.3450i | 0.203312 | + | 0.352146i | 0.949594 | − | 0.313484i | ||
−0.746282 | + | 0.665630i | ||||||||
0 | 0 | |||||||||
33.2933 | − | 57.6656i | 1.13200 | − | 1.96069i | |||||
0 | 0 | |||||||||
−2.46085 | − | 24.5096i | −0.0835748 | − | 0.832388i | |||||
0 | 0 | |||||||||
−14.5202 | − | 25.1497i | −0.492563 | − | 0.853145i | |||||
0 | 0 | |||||||||
−8.54572 | − | 14.8016i | −0.289561 | − | 0.501534i | |||||
0 | 0 | |||||||||
24.6282 | − | 4.99588i | 0.833538 | − | 0.169085i | |||||
0 | 0 | |||||||||
46.6134 | − | 12.6524i | 1.57582 | − | 0.427729i | |||||
0 | 0 | |||||||||
28.3099 | − | 49.0342i | 0.955957 | − | 1.65577i | 0.223794 | − | 0.974636i | ||
0.732163 | − | 0.681130i | ||||||||
0 | 0 | |||||||||
−2.05505 | − | 20.4679i | −0.0693152 | − | 0.690365i | |||||
0 | 0 | |||||||||
−6.41130 | −0.216002 | −0.108001 | − | 0.994151i | ||||||
−0.108001 | + | 0.994151i | ||||||||
0 | 0 | |||||||||
25.7180 | 0.865481 | 0.432741 | − | 0.901518i | ||||||
0.432741 | + | 0.901518i | ||||||||
0 | 0 | |||||||||
−81.3854 | + | 58.5535i | −2.73574 | + | 1.96825i | |||||
0 | 0 | |||||||||
9.99472 | − | 17.3114i | 0.335590 | − | 0.581259i | −0.648008 | − | 0.761633i | ||
0.983598 | + | 0.180375i | ||||||||
0 | 0 | |||||||||
−21.9822 | + | 5.96669i | −0.737261 | + | 0.200116i | |||||
0 | 0 | |||||||||
−14.9744 | + | 6.33591i | −0.501662 | + | 0.212261i | |||||
0 | 0 | |||||||||
−0.917456 | − | 1.58908i | −0.0307015 | − | 0.0531766i | |||||
0 | 0 | |||||||||
37.2051 | + | 64.4412i | 1.24363 | + | 2.15403i | |||||
0 | 0 | |||||||||
7.00118 | + | 3.15623i | 0.233762 | + | 0.105383i | |||||
0 | 0 | |||||||||
12.1724 | − | 21.0832i | 0.405973 | − | 0.703166i | |||||
0 | 0 | |||||||||
2.29104 | + | 3.96819i | 0.0763254 | + | 0.132200i | |||||
0 | 0 | |||||||||
19.9612 | − | 24.5794i | 0.664267 | − | 0.817950i | |||||
0 | 0 | |||||||||
−5.55087 | + | 9.61439i | −0.184517 | + | 0.319593i | |||||
0 | 0 | |||||||||
12.1517 | + | 21.0474i | 0.403491 | + | 0.698866i | 0.994145 | − | 0.108059i | ||
−0.590654 | + | 0.806925i | ||||||||
0 | 0 | |||||||||
7.73809 | − | 23.0825i | 0.256656 | − | 0.765598i | |||||
0 | 0 | |||||||||
−19.7871 | + | 34.2723i | −0.655577 | + | 1.13549i | 0.326171 | + | 0.945311i | ||
−0.981749 | + | 0.190183i | ||||||||
0 | 0 | |||||||||
5.24936 | 0.173728 | |||||||||
0 | 0 | |||||||||
−49.6981 | + | 35.7558i | −1.64297 | + | 1.18205i | |||||
0 | 0 | |||||||||
−1.30536 | + | 4.93571i | −0.0431067 | + | 0.162991i | |||||
0 | 0 | |||||||||
12.9220 | + | 22.3815i | 0.426257 | + | 0.738298i | 0.996537 | − | 0.0831519i | ||
−0.570280 | + | 0.821450i | ||||||||
0 | 0 | |||||||||
−6.21023 | − | 2.79966i | −0.204634 | − | 0.0922518i | |||||
0 | 0 | |||||||||
−4.80251 | − | 8.31818i | −0.158076 | − | 0.273796i | |||||
0 | 0 | |||||||||
15.4481 | − | 26.7569i | 0.507930 | − | 0.879761i | |||||
0 | 0 | |||||||||
−22.1621 | + | 4.49563i | −0.727898 | + | 0.147656i | |||||
0 | 0 | |||||||||
50.8506 | 1.66836 | 0.834178 | − | 0.551496i | ||||||
0.834178 | + | 0.551496i | ||||||||
0 | 0 | |||||||||
0.976100 | + | 0.555132i | 0.0319904 | + | 0.0181937i | |||||
0 | 0 | |||||||||
3.12994 | + | 1.41102i | 0.102470 | + | 0.0461948i | |||||
0 | 0 | |||||||||
5.78315 | − | 10.0167i | 0.189129 | − | 0.327581i | |||||
0 | 0 | |||||||||
32.7623 | 1.07030 | 0.535149 | − | 0.844758i | ||||||
0.535149 | + | 0.844758i | ||||||||
0 | 0 | |||||||||
−32.3689 | − | 14.5923i | −1.05632 | − | 0.476203i | |||||
0 | 0 | |||||||||
50.6793 | 1.65210 | 0.826048 | − | 0.563599i | ||||||
0.826048 | + | 0.563599i | ||||||||
0 | 0 | |||||||||
38.4256 | 1.25131 | |||||||||
0 | 0 | |||||||||
52.7586 | − | 2.19879i | 1.71624 | − | 0.0715267i | |||||
0 | 0 | |||||||||
11.5255 | 0.374530 | 0.187265 | − | 0.982309i | ||||||
0.187265 | + | 0.982309i | ||||||||
0 | 0 | |||||||||
17.2474 | 0.559873 | |||||||||
0 | 0 | |||||||||
−15.0230 | − | 6.77257i | −0.487154 | − | 0.219616i | |||||
0 | 0 | |||||||||
−45.7747 | −1.48279 | −0.741395 | − | 0.671069i | ||||||
−0.741395 | + | 0.671069i | ||||||||
0 | 0 | |||||||||
7.10661 | − | 12.3090i | 0.229965 | − | 0.398310i | |||||
0 | 0 | |||||||||
21.5664 | + | 9.72243i | 0.697142 | + | 0.314281i | |||||
0 | 0 | |||||||||
6.96111 | + | 6.91605i | 0.224786 | + | 0.223331i | |||||
0 | 0 | |||||||||
−20.6302 | −0.665491 | |||||||||
0 | 0 | |||||||||
−5.63990 | + | 16.8237i | −0.181743 | + | 0.542135i | |||||
0 | 0 | |||||||||
24.5188 | − | 42.4678i | 0.789287 | − | 1.36709i | |||||
0 | 0 | |||||||||
4.07666 | + | 7.06098i | 0.131097 | + | 0.227066i | 0.924100 | − | 0.382152i | ||
−0.793003 | + | 0.609218i | ||||||||
0 | 0 | |||||||||
0.422203 | + | 0.190335i | 0.0135631 | + | 0.00611444i | |||||
0 | 0 | |||||||||
−14.1137 | − | 24.4457i | −0.452932 | − | 0.784501i | 0.545635 | − | 0.838023i | ||
−0.998567 | + | 0.0535223i | ||||||||
0 | 0 | |||||||||
−0.505141 | − | 0.501871i | −0.0161941 | − | 0.0160893i | |||||
0 | 0 | |||||||||
18.9975 | − | 13.6679i | 0.608407 | − | 0.437724i | |||||
0 | 0 | |||||||||
−15.6502 | −0.500694 | −0.250347 | − | 0.968156i | ||||||
−0.250347 | + | 0.968156i | ||||||||
0 | 0 | |||||||||
−9.10603 | + | 15.7721i | −0.291030 | + | 0.504079i | |||||
0 | 0 | |||||||||
−26.3675 | + | 5.34871i | −0.841850 | + | 0.170771i | |||||
0 | 0 | |||||||||
1.47581 | + | 2.55617i | 0.0470710 | + | 0.0815293i | 0.888601 | − | 0.458681i | ||
−0.841530 | + | 0.540210i | ||||||||
0 | 0 | |||||||||
−4.69970 | + | 8.14012i | −0.149745 | + | 0.259366i | |||||
0 | 0 | |||||||||
51.7605 | + | 8.27259i | 1.64755 | + | 0.263319i | |||||
0 | 0 | |||||||||
11.0567 | + | 19.1507i | 0.351582 | + | 0.608958i | |||||
0 | 0 | |||||||||
−15.8182 | + | 27.3979i | −0.502482 | + | 0.870324i | 0.497514 | + | 0.867456i | ||
−0.999996 | + | 0.00286819i | ||||||||
0 | 0 | |||||||||
2.41567 | + | 1.08902i | 0.0766588 | + | 0.0345589i | |||||
0 | 0 | |||||||||
−8.63557 | − | 14.9572i | −0.273766 | − | 0.474176i | |||||
0 | 0 | |||||||||
0.792608 | + | 1.37284i | 0.0251021 | + | 0.0434782i | 0.878304 | − | 0.478103i | ||
−0.853201 | + | 0.521582i | ||||||||
0 | 0 | |||||||||
11.1841 | − | 12.0779i | 0.353849 | − | 0.382129i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.q.k.529.2 | 22 | ||
3.2 | odd | 2 | 3024.2.q.k.2881.11 | 22 | |||
4.3 | odd | 2 | 504.2.q.d.25.10 | ✓ | 22 | ||
7.2 | even | 3 | 1008.2.t.k.961.10 | 22 | |||
9.4 | even | 3 | 1008.2.t.k.193.10 | 22 | |||
9.5 | odd | 6 | 3024.2.t.l.1873.1 | 22 | |||
12.11 | even | 2 | 1512.2.q.c.1369.11 | 22 | |||
21.2 | odd | 6 | 3024.2.t.l.289.1 | 22 | |||
28.23 | odd | 6 | 504.2.t.d.457.2 | yes | 22 | ||
36.23 | even | 6 | 1512.2.t.d.361.1 | 22 | |||
36.31 | odd | 6 | 504.2.t.d.193.2 | yes | 22 | ||
63.23 | odd | 6 | 3024.2.q.k.2305.11 | 22 | |||
63.58 | even | 3 | inner | 1008.2.q.k.625.2 | 22 | ||
84.23 | even | 6 | 1512.2.t.d.289.1 | 22 | |||
252.23 | even | 6 | 1512.2.q.c.793.11 | 22 | |||
252.247 | odd | 6 | 504.2.q.d.121.10 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.10 | ✓ | 22 | 4.3 | odd | 2 | ||
504.2.q.d.121.10 | yes | 22 | 252.247 | odd | 6 | ||
504.2.t.d.193.2 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.d.457.2 | yes | 22 | 28.23 | odd | 6 | ||
1008.2.q.k.529.2 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.q.k.625.2 | 22 | 63.58 | even | 3 | inner | ||
1008.2.t.k.193.10 | 22 | 9.4 | even | 3 | |||
1008.2.t.k.961.10 | 22 | 7.2 | even | 3 | |||
1512.2.q.c.793.11 | 22 | 252.23 | even | 6 | |||
1512.2.q.c.1369.11 | 22 | 12.11 | even | 2 | |||
1512.2.t.d.289.1 | 22 | 84.23 | even | 6 | |||
1512.2.t.d.361.1 | 22 | 36.23 | even | 6 | |||
3024.2.q.k.2305.11 | 22 | 63.23 | odd | 6 | |||
3024.2.q.k.2881.11 | 22 | 3.2 | odd | 2 | |||
3024.2.t.l.289.1 | 22 | 21.2 | odd | 6 | |||
3024.2.t.l.1873.1 | 22 | 9.5 | odd | 6 |