Properties

Label 6025.169
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([108,47]))
 
pari: [g,chi] = znchar(Mod(169,6025))
 

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.ik

\(\chi_{6025}(169,\cdot)\) \(\chi_{6025}(294,\cdot)\) \(\chi_{6025}(664,\cdot)\) \(\chi_{6025}(694,\cdot)\) \(\chi_{6025}(889,\cdot)\) \(\chi_{6025}(1009,\cdot)\) \(\chi_{6025}(1039,\cdot)\) \(\chi_{6025}(1264,\cdot)\) \(\chi_{6025}(1379,\cdot)\) \(\chi_{6025}(1434,\cdot)\) \(\chi_{6025}(1554,\cdot)\) \(\chi_{6025}(1579,\cdot)\) \(\chi_{6025}(1669,\cdot)\) \(\chi_{6025}(1684,\cdot)\) \(\chi_{6025}(1754,\cdot)\) \(\chi_{6025}(2089,\cdot)\) \(\chi_{6025}(2189,\cdot)\) \(\chi_{6025}(2459,\cdot)\) \(\chi_{6025}(2669,\cdot)\) \(\chi_{6025}(3084,\cdot)\) \(\chi_{6025}(3644,\cdot)\) \(\chi_{6025}(3779,\cdot)\) \(\chi_{6025}(3859,\cdot)\) \(\chi_{6025}(4044,\cdot)\) \(\chi_{6025}(4109,\cdot)\) \(\chi_{6025}(4169,\cdot)\) \(\chi_{6025}(4529,\cdot)\) \(\chi_{6025}(4534,\cdot)\) \(\chi_{6025}(4629,\cdot)\) \(\chi_{6025}(5379,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{47}{120}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{107}{120}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{23}{120}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{61}{120}\right)\)
value at e.g. 2

Related number fields

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