Properties

Label 6025.244
Modulus $6025$
Conductor $6025$
Order $120$
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([108,91]))
 
pari: [g,chi] = znchar(Mod(244,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
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.ii

\(\chi_{6025}(244,\cdot)\) \(\chi_{6025}(464,\cdot)\) \(\chi_{6025}(494,\cdot)\) \(\chi_{6025}(559,\cdot)\) \(\chi_{6025}(919,\cdot)\) \(\chi_{6025}(1464,\cdot)\) \(\chi_{6025}(2439,\cdot)\) \(\chi_{6025}(2584,\cdot)\) \(\chi_{6025}(2759,\cdot)\) \(\chi_{6025}(2784,\cdot)\) \(\chi_{6025}(2839,\cdot)\) \(\chi_{6025}(2959,\cdot)\) \(\chi_{6025}(2964,\cdot)\) \(\chi_{6025}(3354,\cdot)\) \(\chi_{6025}(3419,\cdot)\) \(\chi_{6025}(3454,\cdot)\) \(\chi_{6025}(3844,\cdot)\) \(\chi_{6025}(4094,\cdot)\) \(\chi_{6025}(4279,\cdot)\) \(\chi_{6025}(4504,\cdot)\) \(\chi_{6025}(4654,\cdot)\) \(\chi_{6025}(4869,\cdot)\) \(\chi_{6025}(4879,\cdot)\) \(\chi_{6025}(4984,\cdot)\) \(\chi_{6025}(4989,\cdot)\) \(\chi_{6025}(5114,\cdot)\) \(\chi_{6025}(5494,\cdot)\) \(\chi_{6025}(5514,\cdot)\) \(\chi_{6025}(5704,\cdot)\) \(\chi_{6025}(5734,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{91}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{31}{120}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{43}{120}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{89}{120}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial