Properties

Label 4011.29
Modulus $4011$
Conductor $573$
Order $190$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(190))
 
M = H._module
 
chi = DirichletCharacter(H, M([95,0,33]))
 
pari: [g,chi] = znchar(Mod(29,4011))
 

Basic properties

Modulus: \(4011\)
Conductor: \(573\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(190\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{573}(29,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4011.bz

\(\chi_{4011}(29,\cdot)\) \(\chi_{4011}(71,\cdot)\) \(\chi_{4011}(113,\cdot)\) \(\chi_{4011}(176,\cdot)\) \(\chi_{4011}(302,\cdot)\) \(\chi_{4011}(323,\cdot)\) \(\chi_{4011}(365,\cdot)\) \(\chi_{4011}(470,\cdot)\) \(\chi_{4011}(533,\cdot)\) \(\chi_{4011}(617,\cdot)\) \(\chi_{4011}(785,\cdot)\) \(\chi_{4011}(806,\cdot)\) \(\chi_{4011}(827,\cdot)\) \(\chi_{4011}(869,\cdot)\) \(\chi_{4011}(890,\cdot)\) \(\chi_{4011}(932,\cdot)\) \(\chi_{4011}(953,\cdot)\) \(\chi_{4011}(974,\cdot)\) \(\chi_{4011}(1016,\cdot)\) \(\chi_{4011}(1079,\cdot)\) \(\chi_{4011}(1100,\cdot)\) \(\chi_{4011}(1142,\cdot)\) \(\chi_{4011}(1247,\cdot)\) \(\chi_{4011}(1289,\cdot)\) \(\chi_{4011}(1310,\cdot)\) \(\chi_{4011}(1394,\cdot)\) \(\chi_{4011}(1436,\cdot)\) \(\chi_{4011}(1478,\cdot)\) \(\chi_{4011}(1520,\cdot)\) \(\chi_{4011}(1604,\cdot)\) ...

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{95})$
Fixed field: Number field defined by a degree 190 polynomial (not computed)

Values on generators

\((2675,2866,2311)\) → \((-1,1,e\left(\frac{33}{190}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 4011 }(29, a) \) \(1\)\(1\)\(e\left(\frac{27}{190}\right)\)\(e\left(\frac{27}{95}\right)\)\(e\left(\frac{7}{38}\right)\)\(e\left(\frac{81}{190}\right)\)\(e\left(\frac{31}{95}\right)\)\(e\left(\frac{5}{19}\right)\)\(e\left(\frac{43}{95}\right)\)\(e\left(\frac{54}{95}\right)\)\(e\left(\frac{99}{190}\right)\)\(e\left(\frac{33}{190}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4011 }(29,a) \;\) at \(\;a = \) e.g. 2