Properties

Label 6025.79
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([4,13]))
 
pari: [g,chi] = znchar(Mod(79,6025))
 

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.ez

\(\chi_{6025}(79,\cdot)\) \(\chi_{6025}(509,\cdot)\) \(\chi_{6025}(839,\cdot)\) \(\chi_{6025}(1089,\cdot)\) \(\chi_{6025}(1144,\cdot)\) \(\chi_{6025}(1494,\cdot)\) \(\chi_{6025}(2844,\cdot)\) \(\chi_{6025}(2939,\cdot)\) \(\chi_{6025}(3054,\cdot)\) \(\chi_{6025}(3194,\cdot)\) \(\chi_{6025}(3379,\cdot)\) \(\chi_{6025}(5014,\cdot)\) \(\chi_{6025}(5034,\cdot)\) \(\chi_{6025}(5584,\cdot)\) \(\chi_{6025}(5779,\cdot)\) \(\chi_{6025}(5984,\cdot)\)

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

\((2652,2176)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{13}{40}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{33}{40}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{7}{40}\right)\)
value at e.g. 2

Related number fields

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