Properties

Label 6025.38
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([228,35]))
 
pari: [g,chi] = znchar(Mod(38,6025))
 

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.jm

\(\chi_{6025}(38,\cdot)\) \(\chi_{6025}(88,\cdot)\) \(\chi_{6025}(153,\cdot)\) \(\chi_{6025}(203,\cdot)\) \(\chi_{6025}(222,\cdot)\) \(\chi_{6025}(252,\cdot)\) \(\chi_{6025}(263,\cdot)\) \(\chi_{6025}(417,\cdot)\) \(\chi_{6025}(547,\cdot)\) \(\chi_{6025}(712,\cdot)\) \(\chi_{6025}(742,\cdot)\) \(\chi_{6025}(1027,\cdot)\) \(\chi_{6025}(1053,\cdot)\) \(\chi_{6025}(1142,\cdot)\) \(\chi_{6025}(1183,\cdot)\) \(\chi_{6025}(1358,\cdot)\) \(\chi_{6025}(1408,\cdot)\) \(\chi_{6025}(1427,\cdot)\) \(\chi_{6025}(1598,\cdot)\) \(\chi_{6025}(1622,\cdot)\) \(\chi_{6025}(1752,\cdot)\) \(\chi_{6025}(1917,\cdot)\) \(\chi_{6025}(1947,\cdot)\) \(\chi_{6025}(2258,\cdot)\) \(\chi_{6025}(2347,\cdot)\) \(\chi_{6025}(2388,\cdot)\) \(\chi_{6025}(2448,\cdot)\) \(\chi_{6025}(2498,\cdot)\) \(\chi_{6025}(2563,\cdot)\) \(\chi_{6025}(2613,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{7}{48}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{79}{120}\right)\)\(e\left(\frac{23}{120}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{203}{240}\right)\)\(e\left(\frac{61}{120}\right)\)\(e\left(\frac{217}{240}\right)\)
value at e.g. 2

Related number fields

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