Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2888,1,Mod(115,2888)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2888, base_ring=CyclotomicField(38))
chi = DirichletCharacter(H, H._module([19, 19, 4]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2888.115");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2888.bb (of order , degree , 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: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Projective image: | |
Projective field: | Galois closure of |
Embedding invariants
Embedding label | 2395.1 | ||
Root | of defining polynomial | ||
Character | 2888.2395 | ||
Dual form | 2888.1.bb.a.1939.1 |
-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 .
0.789141 | + | 0.614213i | 0.789141 | + | 0.614213i | |||||
0.917421 | + | 0.996584i | 0.917421 | + | 0.996584i | 1.00000 | ||||
−0.0825793 | + | 0.996584i | ||||||||
0.245485 | + | 0.969400i | 0.245485 | + | 0.969400i | |||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0.111859 | + | 1.34994i | 0.111859 | + | 1.34994i | |||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
−0.401695 | + | 0.915773i | −0.401695 | + | 0.915773i | |||||
−0.0689406 | + | 0.831990i | −0.0689406 | + | 0.831990i | |||||
0 | 0 | |||||||||
−0.0405441 | − | 0.489294i | −0.0405441 | − | 0.489294i | −0.986361 | − | 0.164595i | ||
0.945817 | − | 0.324699i | ||||||||
−0.740876 | + | 1.13399i | −0.740876 | + | 1.13399i | |||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | |||||
−0.431796 | + | 1.70512i | −0.431796 | + | 1.70512i | 0.245485 | + | 0.969400i | ||
−0.677282 | + | 0.735724i | ||||||||
−0.565423 | + | 0.614213i | −0.565423 | + | 0.614213i | |||||
0.789141 | − | 0.614213i | 0.789141 | − | 0.614213i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.268536 | − | 0.411024i | 0.268536 | − | 0.411024i | |||||
0 | 0 | 0.677282 | − | 0.735724i | ||||||
−0.677282 | + | 0.735724i | ||||||||
−1.28117 | + | 0.439826i | −1.28117 | + | 0.439826i | |||||
0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | |||||
0 | 0 | |||||||||
0.176545 | − | 0.137410i | 0.176545 | − | 0.137410i | |||||
0 | 0 | |||||||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.789141 | − | 0.614213i | ||||||
−0.789141 | + | 0.614213i | ||||||||
−0.986361 | − | 0.164595i | −0.986361 | − | 0.164595i | |||||
0.450427 | − | 0.489294i | 0.450427 | − | 0.489294i | |||||
−1.38806 | + | 1.08037i | −1.38806 | + | 1.08037i | |||||
0 | 0 | |||||||||
−0.823455 | + | 0.137410i | −0.823455 | + | 0.137410i | |||||
0 | 0 | −0.0825793 | − | 0.996584i | ||||||
0.0825793 | + | 0.996584i | ||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.28117 | − | 0.439826i | −1.28117 | − | 0.439826i | −0.401695 | − | 0.915773i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
−1.55676 | + | 0.259777i | −1.55676 | + | 0.259777i | −0.879474 | − | 0.475947i | ||
−0.677282 | + | 0.735724i | ||||||||
0.464369 | − | 0.159418i | 0.464369 | − | 0.159418i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.0825793 | − | 0.996584i | ||||||
0.0825793 | + | 0.996584i | ||||||||
−1.28117 | − | 0.439826i | −1.28117 | − | 0.439826i | |||||
−0.879474 | − | 0.475947i | −0.879474 | − | 0.475947i | |||||
0.945817 | − | 0.324699i | 0.945817 | − | 0.324699i | |||||
−2.09544 | + | 1.13399i | −2.09544 | + | 1.13399i | |||||
0 | 0 | |||||||||
0 | 0 | −0.0825793 | − | 0.996584i | ||||||
0.0825793 | + | 0.996584i | ||||||||
0.223718 | 0.223718 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33609 | + | 0.222954i | 1.33609 | + | 0.222954i | |||||
0 | 0 | |||||||||
1.49277 | + | 0.512467i | 1.49277 | + | 0.512467i | 0.945817 | − | 0.324699i | ||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.677282 | − | 0.735724i | −0.677282 | − | 0.735724i | |||||
0 | 0 | |||||||||
0.655981 | − | 0.109464i | 0.655981 | − | 0.109464i | |||||
0.0663435 | − | 0.151248i | 0.0663435 | − | 0.151248i | −0.879474 | − | 0.475947i | ||
0.945817 | + | 0.324699i | ||||||||
−1.75895 | −1.75895 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.401695 | − | 0.915773i | ||||||
−0.401695 | + | 0.915773i | ||||||||
−0.734221 | − | 0.397341i | −0.734221 | − | 0.397341i | |||||
0.464369 | − | 1.83375i | 0.464369 | − | 1.83375i | −0.0825793 | − | 0.996584i | ||
0.546948 | − | 0.837166i | ||||||||
0 | 0 | |||||||||
1.33609 | − | 0.222954i | 1.33609 | − | 0.222954i | |||||
0.789141 | + | 0.614213i | 0.789141 | + | 0.614213i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.986361 | − | 0.164595i | ||||||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
1.12236 | + | 0.187289i | 1.12236 | + | 0.187289i | |||||
−0.740876 | − | 1.13399i | −0.740876 | − | 1.13399i | |||||
1.54695 | + | 0.837166i | 1.54695 | + | 0.837166i | 1.00000 | ||||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.38806 | − | 0.751179i | −1.38806 | − | 0.751179i | |||||
0 | 0 | |||||||||
0.464369 | + | 0.159418i | 0.464369 | + | 0.159418i | |||||
−0.431796 | − | 1.70512i | −0.431796 | − | 1.70512i | −0.677282 | − | 0.735724i | ||
0.245485 | − | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.740876 | − | 1.13399i | −0.740876 | − | 1.13399i | |||||
−0.803391 | − | 1.83155i | −0.803391 | − | 1.83155i | −0.401695 | − | 0.915773i | ||
−0.401695 | − | 0.915773i | ||||||||
−0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | |||||
0.409883 | 0.409883 | |||||||||
0.945817 | + | 0.324699i | 0.945817 | + | 0.324699i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
−2.35011 | − | 0.392164i | −2.35011 | − | 0.392164i | |||||
0 | 0 | −0.245485 | − | 0.969400i | ||||||
0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.49277 | + | 1.16187i | 1.49277 | + | 1.16187i | 0.945817 | + | 0.324699i | ||
0.546948 | + | 0.837166i | ||||||||
0.176545 | + | 0.137410i | 0.176545 | + | 0.137410i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.387445 | + | 1.52999i | 0.387445 | + | 1.52999i | 0.789141 | + | 0.614213i | ||
−0.401695 | + | 0.915773i | ||||||||
0.917421 | + | 0.996584i | 0.917421 | + | 0.996584i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.863238 | + | 1.32128i | 0.863238 | + | 1.32128i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.748596 | − | 0.124919i | 0.748596 | − | 0.124919i | |||||
0 | 0 | |||||||||
−0.737047 | − | 1.68030i | −0.737047 | − | 1.68030i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−0.0825793 | − | 0.996584i | −0.0825793 | − | 0.996584i | |||||
−1.68709 | − | 1.31311i | −1.68709 | − | 1.31311i | |||||
0 | 0 | |||||||||
−1.38806 | + | 1.08037i | −1.38806 | + | 1.08037i | −0.401695 | + | 0.915773i | ||
−0.986361 | + | 0.164595i | ||||||||
0.584895 | + | 0.316529i | 0.584895 | + | 0.316529i | |||||
0 | 0 | |||||||||
0.145253 | − | 0.0786068i | 0.145253 | − | 0.0786068i | |||||
0 | 0 | |||||||||
−1.38806 | − | 1.08037i | −1.38806 | − | 1.08037i | |||||
0.792434 | − | 1.80657i | 0.792434 | − | 1.80657i | 0.245485 | − | 0.969400i | ||
0.546948 | − | 0.837166i | ||||||||
0 | 0 | |||||||||
−1.07898 | + | 0.180049i | −1.07898 | + | 0.180049i | −0.677282 | − | 0.735724i | ||
−0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.335352 | − | 0.764525i | −0.335352 | − | 0.764525i | |||||
0 | 0 | |||||||||
1.49277 | − | 1.16187i | 1.49277 | − | 1.16187i | |||||
−0.332526 | − | 1.31311i | −0.332526 | − | 1.31311i | |||||
0 | 0 | |||||||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
1.19130 | + | 0.644701i | 1.19130 | + | 0.644701i | |||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
0.245485 | + | 0.969400i | 0.245485 | + | 0.969400i | |||||
−1.38888 | − | 0.476802i | −1.38888 | − | 0.476802i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.770666 | + | 0.837166i | 0.770666 | + | 0.837166i | |||||
0.863238 | + | 0.671885i | 0.863238 | + | 0.671885i | 0.945817 | − | 0.324699i | ||
−0.0825793 | + | 0.996584i | ||||||||
0.111859 | − | 1.34994i | 0.111859 | − | 1.34994i | |||||
0 | 0 | |||||||||
0.706561 | + | 1.61080i | 0.706561 | + | 1.61080i | |||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
−0.0825793 | + | 0.996584i | −0.0825793 | + | 0.996584i | |||||
0 | 0 | |||||||||
0.456615 | + | 0.698901i | 0.456615 | + | 0.698901i | |||||
−0.633988 | − | 1.44535i | −0.633988 | − | 1.44535i | |||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.268536 | + | 0.411024i | 0.268536 | + | 0.411024i | |||||
0.858777 | + | 1.95781i | 0.858777 | + | 1.95781i | |||||
0.706561 | − | 1.61080i | 0.706561 | − | 1.61080i | |||||
−1.55676 | − | 0.259777i | −1.55676 | − | 0.259777i | −0.677282 | − | 0.735724i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.789141 | − | 0.614213i | ||||||
−0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.851814 | + | 0.142143i | 0.851814 | + | 0.142143i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.401695 | − | 0.915773i | ||||||
−0.401695 | + | 0.915773i | ||||||||
0.111859 | − | 1.34994i | 0.111859 | − | 1.34994i | |||||
0.0136387 | + | 0.164595i | 0.0136387 | + | 0.164595i | 1.00000 | ||||
−0.986361 | + | 0.164595i | ||||||||
0.490971 | − | 1.93880i | 0.490971 | − | 1.93880i | |||||
0 | 0 | |||||||||
0.245485 | − | 0.969400i | 0.245485 | − | 0.969400i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
0.323455 | + | 0.251755i | 0.323455 | + | 0.251755i | |||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
0.546948 | + | 0.837166i | 0.546948 | + | 0.837166i | |||||
0.211596 | − | 0.0726411i | 0.211596 | − | 0.0726411i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.61369 | − | 1.75294i | −1.61369 | − | 1.75294i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.332526 | − | 0.361219i | −0.332526 | − | 0.361219i | |||||
0 | 0 | |||||||||
0.706561 | + | 0.382372i | 0.706561 | + | 0.382372i | 0.789141 | − | 0.614213i | ||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.464369 | + | 1.83375i | 0.464369 | + | 1.83375i | |||||
0 | 0 | |||||||||
0.0549195 | + | 0.216872i | 0.0549195 | + | 0.216872i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.25351 | − | 1.21954i | 2.25351 | − | 1.21954i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.789141 | − | 0.614213i | ||||||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0.658807 | + | 0.512770i | 0.658807 | + | 0.512770i | |||||
−0.633988 | + | 1.44535i | −0.633988 | + | 1.44535i | |||||
0.706561 | − | 0.382372i | 0.706561 | − | 0.382372i | −0.0825793 | − | 0.996584i | ||
0.789141 | + | 0.614213i | ||||||||
0.111859 | + | 1.34994i | 0.111859 | + | 1.34994i | |||||
0 | 0 | −0.879474 | − | 0.475947i | ||||||
0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.165159 | − | 1.99317i | −0.165159 | − | 1.99317i | −0.0825793 | − | 0.996584i | ||
−0.0825793 | − | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.130333 | + | 1.57289i | −0.130333 | + | 1.57289i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
−1.28117 | + | 1.39172i | −1.28117 | + | 1.39172i | −0.401695 | + | 0.915773i | ||
−0.879474 | + | 0.475947i | ||||||||
0.667474 | + | 0.361219i | 0.667474 | + | 0.361219i | |||||
0.720667 | + | 1.10306i | 0.720667 | + | 1.10306i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.450427 | − | 1.77870i | 0.450427 | − | 1.77870i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.584895 | + | 2.30970i | 0.584895 | + | 2.30970i | |||||
0 | 0 | |||||||||
−0.0405441 | + | 0.489294i | −0.0405441 | + | 0.489294i | 0.945817 | + | 0.324699i | ||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | |||||
−0.156210 | + | 0.0536269i | −0.156210 | + | 0.0536269i | −0.401695 | − | 0.915773i | ||
0.245485 | + | 0.969400i | ||||||||
−0.524819 | − | 2.07246i | −0.524819 | − | 2.07246i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.75895 | −1.75895 | |||||||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
0.267148 | + | 0.609036i | 0.267148 | + | 0.609036i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.30316 | − | 1.99464i | 1.30316 | − | 1.99464i | |||||
0.162906 | + | 0.0271842i | 0.162906 | + | 0.0271842i | |||||
0 | 0 | −0.879474 | − | 0.475947i | ||||||
0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
−0.431796 | − | 1.70512i | −0.431796 | − | 1.70512i | |||||
0 | 0 | |||||||||
1.73496 | − | 0.938912i | 1.73496 | − | 0.938912i | |||||
−0.431796 | − | 0.233676i | −0.431796 | − | 0.233676i | |||||
0 | 0 | |||||||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
−0.962053 | − | 0.520637i | −0.962053 | − | 0.520637i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.439413 | + | 0.672572i | −0.439413 | + | 0.672572i | −0.986361 | − | 0.164595i | ||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
−1.35456 | + | 1.47145i | −1.35456 | + | 1.47145i | −0.677282 | + | 0.735724i | ||
−0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.204941 | − | 0.809295i | 0.204941 | − | 0.809295i | |||||
−1.84153 | − | 0.996584i | −1.84153 | − | 0.996584i | |||||
0 | 0 | |||||||||
1.08824 | − | 2.48095i | 1.08824 | − | 2.48095i | |||||
1.89163 | 1.89163 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0.544122 | − | 1.24047i | 0.544122 | − | 1.24047i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0743919 | − | 0.0808112i | −0.0743919 | − | 0.0808112i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.544122 | + | 1.24047i | 0.544122 | + | 1.24047i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.401695 | + | 0.915773i | −0.401695 | + | 0.915773i | |||||
0 | 0 | |||||||||
−0.803162 | − | 1.22933i | −0.803162 | − | 1.22933i | |||||
−1.35456 | −1.35456 | −0.677282 | − | 0.735724i | ||||||
−0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
−1.86584 | − | 0.640542i | −1.86584 | − | 0.640542i | −0.986361 | − | 0.164595i | ||
−0.879474 | − | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.211596 | + | 2.55359i | 0.211596 | + | 2.55359i | |||||
0 | 0 | |||||||||
0.706561 | + | 1.61080i | 0.706561 | + | 1.61080i | |||||
0.0939655 | + | 1.13399i | 0.0939655 | + | 1.13399i | |||||
0 | 0 | |||||||||
0.268536 | + | 1.06042i | 0.268536 | + | 1.06042i | |||||
0 | 0 | |||||||||
0.917421 | − | 0.996584i | 0.917421 | − | 0.996584i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.439413 | − | 0.672572i | −0.439413 | − | 0.672572i | 0.546948 | − | 0.837166i | ||
−0.986361 | + | 0.164595i | ||||||||
−0.431796 | + | 1.70512i | −0.431796 | + | 1.70512i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.03463 | − | 0.355188i | 1.03463 | − | 0.355188i | 0.245485 | − | 0.969400i | ||
0.789141 | + | 0.614213i | ||||||||
−0.677282 | + | 0.735724i | −0.677282 | + | 0.735724i | |||||
−1.16931 | + | 1.78976i | −1.16931 | + | 1.78976i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0689406 | + | 0.831990i | −0.0689406 | + | 0.831990i | |||||
0 | 0 | |||||||||
0.387445 | − | 1.52999i | 0.387445 | − | 1.52999i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.387445 | − | 0.301561i | 0.387445 | − | 0.301561i | −0.401695 | − | 0.915773i | ||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.546948 | − | 0.837166i | ||||||
−0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0405441 | + | 0.489294i | −0.0405441 | + | 0.489294i | |||||
−0.439413 | + | 1.00176i | −0.439413 | + | 1.00176i | 0.546948 | + | 0.837166i | ||
−0.986361 | + | 0.164595i | ||||||||
−0.524819 | + | 2.07246i | −0.524819 | + | 2.07246i | |||||
0 | 0 | |||||||||
1.54695 | − | 0.837166i | 1.54695 | − | 0.837166i | |||||
0 | 0 | |||||||||
−1.06894 | − | 1.16118i | −1.06894 | − | 1.16118i | |||||
0 | 0 | −0.789141 | − | 0.614213i | ||||||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0.245485 | − | 0.969400i | 0.245485 | − | 0.969400i | |||||
0 | 0 | |||||||||
0.811270 | + | 0.631437i | 0.811270 | + | 0.631437i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.0825793 | − | 0.996584i | ||||||
0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0.454255 | − | 1.03560i | 0.454255 | − | 1.03560i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.546948 | − | 0.837166i | ||||||
−0.546948 | + | 0.837166i | ||||||||
0.584895 | + | 0.635365i | 0.584895 | + | 0.635365i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.111859 | − | 0.121511i | 0.111859 | − | 0.121511i | −0.677282 | − | 0.735724i | ||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.546948 | − | 0.837166i | ||||||
−0.546948 | + | 0.837166i | ||||||||
0.917421 | − | 0.996584i | 0.917421 | − | 0.996584i | |||||
0 | 0 | |||||||||
−0.0903332 | + | 0.138265i | −0.0903332 | + | 0.138265i | |||||
−0.108808 | − | 1.31311i | −0.108808 | − | 1.31311i | |||||
1.57828 | − | 1.22843i | 1.57828 | − | 1.22843i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.789141 | − | 0.614213i | 0.789141 | − | 0.614213i | |||||
−2.35011 | − | 0.392164i | −2.35011 | − | 0.392164i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.100620 | + | 0.397341i | 0.100620 | + | 0.397341i | |||||
0 | 0 | 0.986361 | − | 0.164595i | ||||||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0825793 | + | 0.996584i | −0.0825793 | + | 0.996584i | |||||
0.162906 | + | 1.96598i | 0.162906 | + | 1.96598i | 0.245485 | + | 0.969400i | ||
−0.0825793 | + | 0.996584i | ||||||||
0.211596 | + | 0.0726411i | 0.211596 | + | 0.0726411i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.196754 | − | 2.37447i | −0.196754 | − | 2.37447i | |||||
−0.759861 | − | 0.260861i | −0.759861 | − | 0.260861i | −0.0825793 | − | 0.996584i | ||
−0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
2.52739 | − | 0.867655i | 2.52739 | − | 0.867655i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.16931 | − | 0.910111i | −1.16931 | − | 0.910111i | |||||
−0.0405441 | − | 0.489294i | −0.0405441 | − | 0.489294i | |||||
0.387445 | − | 0.301561i | 0.387445 | − | 0.301561i | −0.401695 | − | 0.915773i | ||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
0.322718 | + | 0.735724i | 0.322718 | + | 0.735724i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.19130 | + | 1.29410i | 1.19130 | + | 1.29410i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.759861 | + | 1.73231i | −0.759861 | + | 1.73231i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.401695 | − | 0.915773i | ||||||
−0.401695 | + | 0.915773i | ||||||||
−0.0898664 | + | 0.204875i | −0.0898664 | + | 0.204875i | |||||
1.19130 | + | 0.644701i | 1.19130 | + | 0.644701i | 0.945817 | − | 0.324699i | ||
0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.52739 | + | 0.421747i | 2.52739 | + | 0.421747i | |||||
0 | 0 | 0.677282 | − | 0.735724i | ||||||
−0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0.456615 | − | 0.698901i | 0.456615 | − | 0.698901i | |||||
0 | 0 | |||||||||
0.863238 | + | 1.32128i | 0.863238 | + | 1.32128i | 0.945817 | + | 0.324699i | ||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.28117 | − | 0.439826i | −1.28117 | − | 0.439826i | −0.401695 | − | 0.915773i | ||
−0.879474 | + | 0.475947i | ||||||||
0.204941 | + | 0.809295i | 0.204941 | + | 0.809295i | |||||
−0.163260 | + | 0.644701i | −0.163260 | + | 0.644701i | |||||
−1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | |||||
0 | 0 | |||||||||
0.792434 | + | 0.132234i | 0.792434 | + | 0.132234i | |||||
0 | 0 | |||||||||
−0.740876 | + | 1.13399i | −0.740876 | + | 1.13399i | |||||
−0.439413 | − | 0.672572i | −0.439413 | − | 0.672572i | 0.546948 | − | 0.837166i | ||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0.158070 | + | 0.360364i | 0.158070 | + | 0.360364i | |||||
0 | 0 | |||||||||
0 | 0 | −0.945817 | − | 0.324699i | ||||||
0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.986361 | − | 0.164595i | ||||||
0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.09390 | − | 1.67433i | 1.09390 | − | 1.67433i | |||||
1.03463 | − | 1.58361i | 1.03463 | − | 1.58361i | 0.245485 | − | 0.969400i | ||
0.789141 | − | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.06894 | + | 1.16118i | −1.06894 | + | 1.16118i | |||||
0.190224 | + | 0.751179i | 0.190224 | + | 0.751179i | |||||
0 | 0 | |||||||||
−0.0825793 | − | 0.996584i | −0.0825793 | − | 0.996584i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.546948 | − | 0.837166i | ||||||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.86584 | + | 0.311353i | −1.86584 | + | 0.311353i | |||||
0 | 0 | |||||||||
0.304866 | + | 0.695024i | 0.304866 | + | 0.695024i | |||||
0 | 0 | |||||||||
−0.108808 | + | 1.31311i | −0.108808 | + | 1.31311i | |||||
0 | 0 | −0.546948 | − | 0.837166i | ||||||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0.122362 | + | 1.47669i | 0.122362 | + | 1.47669i | |||||
0 | 0 | |||||||||
−1.07898 | − | 1.65150i | −1.07898 | − | 1.65150i | −0.677282 | − | 0.735724i | ||
−0.401695 | − | 0.915773i | ||||||||
1.44795 | − | 1.12698i | 1.44795 | − | 1.12698i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.957082 | + | 2.18193i | −0.957082 | + | 2.18193i | |||||
−0.633988 | − | 0.493453i | −0.633988 | − | 0.493453i | 0.245485 | − | 0.969400i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.332526 | + | 0.361219i | −0.332526 | + | 0.361219i | |||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.06894 | + | 0.831990i | −1.06894 | + | 0.831990i | |||||
0 | 0 | |||||||||
0 | 0 | 0.945817 | − | 0.324699i | ||||||
−0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.945817 | − | 0.324699i | 0.945817 | − | 0.324699i | |||||
0.0549195 | − | 0.216872i | 0.0549195 | − | 0.216872i | |||||
−0.156210 | − | 0.0536269i | −0.156210 | − | 0.0536269i | |||||
0 | 0 | |||||||||
0.858777 | − | 1.95781i | 0.858777 | − | 1.95781i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.464369 | − | 0.159418i | 0.464369 | − | 0.159418i | −0.0825793 | − | 0.996584i | ||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
1.19130 | + | 1.29410i | 1.19130 | + | 1.29410i | 0.945817 | + | 0.324699i | ||
0.245485 | + | 0.969400i | ||||||||
−1.38806 | − | 1.08037i | −1.38806 | − | 1.08037i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.163260 | + | 0.644701i | −0.163260 | + | 0.644701i | |||||
−0.0825793 | − | 0.996584i | −0.0825793 | − | 0.996584i | |||||
0 | 0 | |||||||||
−0.529280 | + | 1.20664i | −0.529280 | + | 1.20664i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.25351 | − | 0.773631i | 2.25351 | − | 0.773631i | |||||
0 | 0 | |||||||||
0.111859 | + | 0.121511i | 0.111859 | + | 0.121511i | |||||
−1.16931 | − | 1.78976i | −1.16931 | − | 1.78976i | |||||
0 | 0 | |||||||||
−0.197221 | + | 0.449618i | −0.197221 | + | 0.449618i | |||||
0 | 0 | |||||||||
0 | 0 | 0.789141 | − | 0.614213i | ||||||
−0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.706561 | − | 1.61080i | 0.706561 | − | 1.61080i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.111859 | + | 0.121511i | 0.111859 | + | 0.121511i | 0.789141 | − | 0.614213i | ||
−0.677282 | + | 0.735724i | ||||||||
1.94582 | + | 0.324699i | 1.94582 | + | 0.324699i | |||||
0 | 0 | |||||||||
−0.197221 | − | 0.449618i | −0.197221 | − | 0.449618i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.439413 | − | 1.00176i | −0.439413 | − | 1.00176i | |||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.639815 | + | 0.979309i | 0.639815 | + | 0.979309i | |||||
−0.759861 | + | 0.260861i | −0.759861 | + | 0.260861i | |||||
−1.28117 | + | 1.39172i | −1.28117 | + | 1.39172i | −0.401695 | + | 0.915773i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.97272 | + | 0.329189i | −1.97272 | + | 0.329189i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.86584 | − | 0.640542i | −1.86584 | − | 0.640542i | −0.986361 | − | 0.164595i | ||
−0.879474 | − | 0.475947i | ||||||||
0 | 0 | |||||||||
1.78914 | − | 0.614213i | 1.78914 | − | 0.614213i | 0.789141 | − | 0.614213i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.658807 | − | 0.512770i | 0.658807 | − | 0.512770i | |||||
−0.332526 | − | 1.31311i | −0.332526 | − | 1.31311i | −0.879474 | − | 0.475947i | ||
0.546948 | − | 0.837166i | ||||||||
−0.841109 | − | 1.91753i | −0.841109 | − | 1.91753i | |||||
−0.151520 | + | 0.164595i | −0.151520 | + | 0.164595i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.38261 | − | 1.28940i | 2.38261 | − | 1.28940i | |||||
0 | 0 | |||||||||
1.49277 | + | 1.16187i | 1.49277 | + | 1.16187i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.197221 | + | 0.449618i | −0.197221 | + | 0.449618i | −0.986361 | − | 0.164595i | ||
0.789141 | + | 0.614213i | ||||||||
1.19130 | − | 0.644701i | 1.19130 | − | 0.644701i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.863238 | + | 0.671885i | 0.863238 | + | 0.671885i | 0.945817 | − | 0.324699i | ||
−0.0825793 | + | 0.996584i | ||||||||
−0.00907043 | − | 0.109464i | −0.00907043 | − | 0.109464i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
−0.332526 | + | 1.31311i | −0.332526 | + | 1.31311i | |||||
−1.97272 | + | 0.329189i | −1.97272 | + | 0.329189i | −0.986361 | + | 0.164595i | ||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0.121263 | + | 0.0656242i | 0.121263 | + | 0.0656242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
−0.879474 | + | 0.475947i | −0.879474 | + | 0.475947i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.121263 | − | 1.46343i | 0.121263 | − | 1.46343i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
−1.06894 | − | 0.831990i | −1.06894 | − | 0.831990i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.962053 | + | 1.47253i | −0.962053 | + | 1.47253i | −0.0825793 | + | 0.996584i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
−0.197221 | − | 0.778807i | −0.197221 | − | 0.778807i | −0.986361 | − | 0.164595i | ||
0.789141 | − | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | |||||
−1.07898 | − | 1.65150i | −1.07898 | − | 1.65150i | |||||
0.0549195 | − | 0.662780i | 0.0549195 | − | 0.662780i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0.267148 | + | 1.05494i | 0.267148 | + | 1.05494i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.55676 | − | 0.259777i | −1.55676 | − | 0.259777i | −0.677282 | − | 0.735724i | ||
−0.879474 | + | 0.475947i | ||||||||
−1.40147 | + | 2.14510i | −1.40147 | + | 2.14510i | |||||
−1.86584 | + | 0.311353i | −1.86584 | + | 0.311353i | −0.986361 | − | 0.164595i | ||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.431796 | + | 1.70512i | −0.431796 | + | 1.70512i | |||||
0 | 0 | 0.986361 | − | 0.164595i | ||||||
−0.986361 | + | 0.164595i | ||||||||
−0.622362 | + | 0.952596i | −0.622362 | + | 0.952596i | |||||
0.190224 | − | 0.751179i | 0.190224 | − | 0.751179i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.439413 | + | 1.00176i | −0.439413 | + | 1.00176i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33609 | − | 0.222954i | 1.33609 | − | 0.222954i | |||||
1.49365 | + | 0.512770i | 1.49365 | + | 0.512770i | |||||
0 | 0 | |||||||||
0.464369 | + | 0.159418i | 0.464369 | + | 0.159418i | 0.546948 | − | 0.837166i | ||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
0.0663435 | − | 0.800647i | 0.0663435 | − | 0.800647i | |||||
0 | 0 | |||||||||
−1.38806 | + | 1.08037i | −1.38806 | + | 1.08037i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.19130 | + | 0.644701i | 1.19130 | + | 0.644701i | 0.945817 | − | 0.324699i | ||
0.245485 | + | 0.969400i | ||||||||
1.03463 | + | 0.355188i | 1.03463 | + | 0.355188i | |||||
−0.0184745 | − | 0.222954i | −0.0184745 | − | 0.222954i | |||||
−0.986361 | + | 0.164595i | −0.986361 | + | 0.164595i | |||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
−2.02204 | + | 0.694169i | −2.02204 | + | 0.694169i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.02928 | + | 0.353352i | 1.02928 | + | 0.353352i | |||||
0 | 0 | |||||||||
0.111859 | − | 1.34994i | 0.111859 | − | 1.34994i | −0.677282 | − | 0.735724i | ||
0.789141 | − | 0.614213i | ||||||||
−0.565423 | + | 0.614213i | −0.565423 | + | 0.614213i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.24549 | − | 0.969400i | 1.24549 | − | 0.969400i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.130333 | + | 0.101443i | −0.130333 | + | 0.101443i | −0.677282 | − | 0.735724i | ||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.490971 | 0.490971 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.30316 | − | 1.99464i | 1.30316 | − | 1.99464i | |||||
0 | 0 | |||||||||
1.83484 | − | 1.99317i | 1.83484 | − | 1.99317i | |||||
0 | 0 | |||||||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.332526 | + | 0.361219i | −0.332526 | + | 0.361219i | |||||
0 | 0 | |||||||||
−0.962053 | + | 0.520637i | −0.962053 | + | 0.520637i | |||||
0 | 0 | |||||||||
−1.68709 | + | 1.31311i | −1.68709 | + | 1.31311i | |||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.73496 | + | 0.289513i | 1.73496 | + | 0.289513i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.130333 | − | 1.57289i | −0.130333 | − | 1.57289i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.677282 | − | 0.735724i | ||||||
0.677282 | + | 0.735724i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.789141 | − | 0.614213i | 0.789141 | − | 0.614213i | |||||
−2.56234 | −2.56234 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.252369 | + | 0.996584i | 0.252369 | + | 0.996584i | |||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
−0.158807 | + | 0.627115i | −0.158807 | + | 0.627115i | |||||
0 | 0 | |||||||||
0.229250 | − | 2.76663i | 0.229250 | − | 2.76663i | |||||
0 | 0 | |||||||||
0 | 0 | −0.0825793 | − | 0.996584i | ||||||
0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0766945 | − | 0.0263293i | −0.0766945 | − | 0.0263293i | |||||
0.994549 | − | 0.538223i | 0.994549 | − | 0.538223i | |||||
0.268536 | − | 1.06042i | 0.268536 | − | 1.06042i | −0.677282 | − | 0.735724i | ||
0.945817 | − | 0.324699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.803162 | + | 1.22933i | −0.803162 | + | 1.22933i | |||||
0.0713149 | + | 0.860643i | 0.0713149 | + | 0.860643i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
−0.524819 | + | 0.408483i | −0.524819 | + | 0.408483i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.245485 | − | 0.969400i | ||||||
0.245485 | + | 0.969400i | ||||||||
0.162906 | − | 0.0271842i | 0.162906 | − | 0.0271842i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.156210 | + | 1.88517i | −0.156210 | + | 1.88517i | 0.245485 | + | 0.969400i | ||
−0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33609 | − | 0.222954i | 1.33609 | − | 0.222954i | |||||
0.0136387 | + | 0.164595i | 0.0136387 | + | 0.164595i | 1.00000 | ||||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
−0.196754 | − | 0.106478i | −0.196754 | − | 0.106478i | |||||
−0.156210 | + | 0.0536269i | −0.156210 | + | 0.0536269i | |||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0.720667 | − | 1.10306i | 0.720667 | − | 1.10306i | |||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.28117 | + | 0.439826i | −1.28117 | + | 0.439826i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
−1.61369 | − | 1.75294i | −1.61369 | − | 1.75294i | |||||
−0.156210 | − | 0.0536269i | −0.156210 | − | 0.0536269i | 0.245485 | − | 0.969400i | ||
−0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.164648 | + | 0.375360i | −0.164648 | + | 0.375360i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.986361 | − | 0.164595i | ||||||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.677282 | + | 0.735724i | −0.677282 | + | 0.735724i | |||||
1.44841 | − | 0.241698i | 1.44841 | − | 0.241698i | |||||
−1.07898 | + | 1.65150i | −1.07898 | + | 1.65150i | |||||
−0.916071 | − | 0.152865i | −0.916071 | − | 0.152865i | |||||
0.122362 | + | 0.187289i | 0.122362 | + | 0.187289i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.19130 | − | 0.644701i | 1.19130 | − | 0.644701i | 0.245485 | − | 0.969400i | ||
0.945817 | + | 0.324699i | ||||||||
0 | 0 | |||||||||
0.464369 | + | 1.83375i | 0.464369 | + | 1.83375i | 0.546948 | + | 0.837166i | ||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.30316 | − | 1.99464i | 1.30316 | − | 1.99464i | |||||
−1.06894 | + | 1.16118i | −1.06894 | + | 1.16118i | |||||
−0.439413 | − | 0.672572i | −0.439413 | − | 0.672572i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
2.52739 | + | 0.867655i | 2.52739 | + | 0.867655i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
−0.163260 | − | 0.644701i | −0.163260 | − | 0.644701i | |||||
0 | 0 | |||||||||
−0.740876 | + | 1.13399i | −0.740876 | + | 1.13399i | 0.245485 | + | 0.969400i | ||
−0.986361 | + | 0.164595i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.789141 | − | 0.614213i | ||||||
0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.19130 | − | 1.29410i | 1.19130 | − | 1.29410i | |||||
−0.363749 | − | 1.43641i | −0.363749 | − | 1.43641i | |||||
0 | 0 | |||||||||
0.268536 | − | 0.411024i | 0.268536 | − | 0.411024i | |||||
0 | 0 | |||||||||
0.490971 | 0.490971 | |||||||||
0 | 0 | 0.789141 | − | 0.614213i | ||||||
−0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
−0.879474 | − | 0.475947i | −0.879474 | − | 0.475947i | |||||
0 | 0 | |||||||||
−1.07340 | + | 0.179119i | −1.07340 | + | 0.179119i | |||||
−0.197221 | + | 0.778807i | −0.197221 | + | 0.778807i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.70913 | −2.70913 | |||||||||
0.145253 | + | 1.75294i | 0.145253 | + | 1.75294i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.789141 | − | 0.614213i | ||||||
−0.789141 | + | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.66364 | + | 0.900319i | −1.66364 | + | 0.900319i | |||||
0.322718 | − | 0.735724i | 0.322718 | − | 0.735724i | −0.677282 | − | 0.735724i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0.706561 | − | 1.61080i | 0.706561 | − | 1.61080i | −0.0825793 | − | 0.996584i | ||
0.789141 | − | 0.614213i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.677282 | − | 0.735724i | ||||||
−0.677282 | + | 0.735724i | ||||||||
−0.196754 | + | 0.106478i | −0.196754 | + | 0.106478i | |||||
0 | 0 | |||||||||
0.544122 | + | 1.24047i | 0.544122 | + | 1.24047i | |||||
−0.696274 | − | 2.74952i | −0.696274 | − | 2.74952i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57921 | − | 0.542145i | 1.57921 | − | 0.542145i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.73542 | + | 1.88517i | 1.73542 | + | 1.88517i | |||||
0 | 0 | 0.401695 | − | 0.915773i | ||||||
−0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.06894 | + | 1.16118i | −1.06894 | + | 1.16118i | −0.0825793 | + | 0.996584i | ||
−0.986361 | + | 0.164595i | ||||||||
0.789607 | − | 0.271073i | 0.789607 | − | 0.271073i | |||||
−0.962053 | − | 1.47253i | −0.962053 | − | 1.47253i | −0.879474 | − | 0.475947i | ||
−0.0825793 | − | 0.996584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.130333 | + | 1.57289i | −0.130333 | + | 1.57289i | |||||
0 | 0 | 0.245485 | − | 0.969400i | ||||||
−0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0461343 | − | 0.556759i | 0.0461343 | − | 0.556759i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.740876 | − | 1.13399i | −0.740876 | − | 1.13399i | |||||
0 | 0 | |||||||||
−0.335352 | + | 0.764525i | −0.335352 | + | 0.764525i | |||||
0 | 0 | |||||||||
−0.524819 | + | 0.408483i | −0.524819 | + | 0.408483i | |||||
0 | 0 | |||||||||
−1.55676 | − | 0.259777i | −1.55676 | − | 0.259777i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.598305 | + | 0.915773i | 0.598305 | + | 0.915773i | 1.00000 | ||||
−0.401695 | + | 0.915773i | ||||||||
0.544122 | + | 0.591074i | 0.544122 | + | 0.591074i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.401695 | − | 0.915773i | ||||||
0.401695 | + | 0.915773i | ||||||||
−1.28117 | + | 0.439826i | −1.28117 | + | 0.439826i | |||||
0.346901 | − | 0.790855i | 0.346901 | − | 0.790855i | |||||
0.0663435 | − | 0.800647i | 0.0663435 | − | 0.800647i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0966005 | + | 0.381467i | −0.0966005 | + | 0.381467i | |||||
0 | 0 | 0.0825793 | − | 0.996584i | ||||||
−0.0825793 | + | 0.996584i | ||||||||
0 | 0 | |||||||||
−1.24270 | − | 1.34994i | −1.24270 | − | 1.34994i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33609 | + | 1.45138i | 1.33609 | + | 1.45138i | 0.789141 | + | 0.614213i | ||
0.546948 | + | 0.837166i | ||||||||
0 | 0 | |||||||||
−0.986361 | + | 0.164595i | −0.986361 | + | 0.164595i | |||||
1.89163 | − | 0.649399i | 1.89163 | − | 0.649399i | |||||
0 | 0 | |||||||||
1.78914 | − | 0.614213i | 1.78914 | − | 0.614213i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.24549 | − | 0.969400i | 1.24549 | − | 0.969400i | 0.245485 | − | 0.969400i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
−1.07340 | − | 2.44711i | −1.07340 | − | 2.44711i | |||||
0 | 0 | |||||||||
0 | 0 | 0.879474 | − | 0.475947i | ||||||
−0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.55676 | + | 0.259777i | −1.55676 | + | 0.259777i | |||||
0 | 0 | |||||||||
−0.311270 | + | 0.709624i | −0.311270 | + | 0.709624i | |||||
1.24549 | + | 0.969400i | 1.24549 | + | 0.969400i | 1.00000 | ||||
0.245485 | + | 0.969400i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.546948 | − | 0.837166i | 0.546948 | − | 0.837166i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.598305 | + | 0.915773i | 0.598305 | + | 0.915773i | 1.00000 | ||||
−0.401695 | + | 0.915773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.245485 | − | 0.969400i | 0.245485 | − | 0.969400i | |||||
0 | 0 | |||||||||
−1.06957 | + | 1.16187i | −1.06957 | + | 1.16187i | |||||
−1.66364 | − | 0.900319i | −1.66364 | − | 0.900319i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−0.186311 | + | 0.735724i | −0.186311 | + | 0.735724i | |||||
−0.957082 | + | 2.18193i | −0.957082 | + | 2.18193i | |||||
0 | 0 | |||||||||
0.490971 | + | 1.93880i | 0.490971 | + | 1.93880i | 0.245485 | + | 0.969400i | ||
0.245485 | + | 0.969400i | ||||||||
−0.892396 | + | 0.969400i | −0.892396 | + | 0.969400i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.07898 | + | 1.65150i | −1.07898 | + | 1.65150i | −0.401695 | + | 0.915773i | ||
−0.677282 | + | 0.735724i | ||||||||
−0.810441 | + | 1.24047i | −0.810441 | + | 1.24047i | |||||
−0.816800 | + | 0.280408i | −0.816800 | + | 0.280408i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.162906 | − | 1.96598i | 0.162906 | − | 1.96598i | |||||
0 | 0 | −0.945817 | − | 0.324699i | ||||||
0.945817 | + | 0.324699i | ||||||||
1.83484 | 1.83484 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.879474 | − | 0.475947i | ||||||
0.879474 | + | 0.475947i | ||||||||
0 | 0 | |||||||||
0.267148 | − | 1.05494i | 0.267148 | − | 1.05494i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.09544 | + | 1.13399i | −2.09544 | + | 1.13399i | |||||
0 | 0 | −0.879474 | − | 0.475947i | ||||||
0.879474 | + | 0.475947i | ||||||||
−0.197221 | − | 0.778807i | −0.197221 | − | 0.778807i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2888.1.bb.a.2395.1 | yes | 18 | |
8.3 | odd | 2 | CM | 2888.1.bb.a.2395.1 | yes | 18 | |
361.134 | even | 19 | inner | 2888.1.bb.a.1939.1 | ✓ | 18 | |
2888.1939 | odd | 38 | inner | 2888.1.bb.a.1939.1 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2888.1.bb.a.1939.1 | ✓ | 18 | 361.134 | even | 19 | inner | |
2888.1.bb.a.1939.1 | ✓ | 18 | 2888.1939 | odd | 38 | inner | |
2888.1.bb.a.2395.1 | yes | 18 | 1.1 | even | 1 | trivial | |
2888.1.bb.a.2395.1 | yes | 18 | 8.3 | odd | 2 | CM |