Properties

Modulus 1157
Conductor 1157
Order 44
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1157.bj

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1157)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([11,41]))
 
pari: [g,chi] = znchar(Mod(21,1157))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1157
Conductor = 1157
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 44
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1157.bj
Orbit index = 36

Galois orbit

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

\(\chi_{1157}(5,\cdot)\) \(\chi_{1157}(21,\cdot)\) \(\chi_{1157}(109,\cdot)\) \(\chi_{1157}(125,\cdot)\) \(\chi_{1157}(138,\cdot)\) \(\chi_{1157}(346,\cdot)\) \(\chi_{1157}(398,\cdot)\) \(\chi_{1157}(463,\cdot)\) \(\chi_{1157}(525,\cdot)\) \(\chi_{1157}(551,\cdot)\) \(\chi_{1157}(606,\cdot)\) \(\chi_{1157}(632,\cdot)\) \(\chi_{1157}(694,\cdot)\) \(\chi_{1157}(759,\cdot)\) \(\chi_{1157}(811,\cdot)\) \(\chi_{1157}(1019,\cdot)\) \(\chi_{1157}(1032,\cdot)\) \(\chi_{1157}(1048,\cdot)\) \(\chi_{1157}(1136,\cdot)\) \(\chi_{1157}(1152,\cdot)\)

Values on generators

\((535,92)\) → \((i,e\left(\frac{41}{44}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{1}{44}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)