Properties

Label 6025.167
Modulus $6025$
Conductor $6025$
Order $240$
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([156,143]))
 
pari: [g,chi] = znchar(Mod(167,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.jc

\(\chi_{6025}(167,\cdot)\) \(\chi_{6025}(227,\cdot)\) \(\chi_{6025}(248,\cdot)\) \(\chi_{6025}(283,\cdot)\) \(\chi_{6025}(312,\cdot)\) \(\chi_{6025}(378,\cdot)\) \(\chi_{6025}(448,\cdot)\) \(\chi_{6025}(533,\cdot)\) \(\chi_{6025}(833,\cdot)\) \(\chi_{6025}(998,\cdot)\) \(\chi_{6025}(1063,\cdot)\) \(\chi_{6025}(1078,\cdot)\) \(\chi_{6025}(1198,\cdot)\) \(\chi_{6025}(1477,\cdot)\) \(\chi_{6025}(1483,\cdot)\) \(\chi_{6025}(1502,\cdot)\) \(\chi_{6025}(1588,\cdot)\) \(\chi_{6025}(1592,\cdot)\) \(\chi_{6025}(1742,\cdot)\) \(\chi_{6025}(1753,\cdot)\) \(\chi_{6025}(2103,\cdot)\) \(\chi_{6025}(2298,\cdot)\) \(\chi_{6025}(2348,\cdot)\) \(\chi_{6025}(2397,\cdot)\) \(\chi_{6025}(2567,\cdot)\) \(\chi_{6025}(2697,\cdot)\) \(\chi_{6025}(2778,\cdot)\) \(\chi_{6025}(3062,\cdot)\) \(\chi_{6025}(3063,\cdot)\) \(\chi_{6025}(3077,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{143}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{103}{120}\right)\)\(e\left(\frac{119}{120}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{203}{240}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{71}{240}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{17}{48}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial