Properties

Label 6025.236
Modulus $6025$
Conductor $6025$
Order $40$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6025)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([32,3]))
 
pari: [g,chi] = znchar(Mod(236,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.ew

\(\chi_{6025}(236,\cdot)\) \(\chi_{6025}(561,\cdot)\) \(\chi_{6025}(696,\cdot)\) \(\chi_{6025}(916,\cdot)\) \(\chi_{6025}(1246,\cdot)\) \(\chi_{6025}(1266,\cdot)\) \(\chi_{6025}(1646,\cdot)\) \(\chi_{6025}(1881,\cdot)\) \(\chi_{6025}(2196,\cdot)\) \(\chi_{6025}(3536,\cdot)\) \(\chi_{6025}(3731,\cdot)\) \(\chi_{6025}(3861,\cdot)\) \(\chi_{6025}(3981,\cdot)\) \(\chi_{6025}(5241,\cdot)\) \(\chi_{6025}(5591,\cdot)\) \(\chi_{6025}(5831,\cdot)\)

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

Values on generators

\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{3}{40}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{20}\right)\)\(i\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{3}{20}\right)\)\(-1\)\(e\left(\frac{27}{40}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{29}{40}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: Number field defined by a degree 40 polynomial