Properties

Label 6025.197
Modulus $6025$
Conductor $6025$
Order $80$
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([68,15]))
 
pari: [g,chi] = znchar(Mod(197,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(80\)
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.hd

\(\chi_{6025}(197,\cdot)\) \(\chi_{6025}(317,\cdot)\) \(\chi_{6025}(608,\cdot)\) \(\chi_{6025}(647,\cdot)\) \(\chi_{6025}(767,\cdot)\) \(\chi_{6025}(838,\cdot)\) \(\chi_{6025}(853,\cdot)\) \(\chi_{6025}(1402,\cdot)\) \(\chi_{6025}(1522,\cdot)\) \(\chi_{6025}(1798,\cdot)\) \(\chi_{6025}(1813,\cdot)\) \(\chi_{6025}(1852,\cdot)\) \(\chi_{6025}(1972,\cdot)\) \(\chi_{6025}(2058,\cdot)\) \(\chi_{6025}(2727,\cdot)\) \(\chi_{6025}(3003,\cdot)\) \(\chi_{6025}(3177,\cdot)\) \(\chi_{6025}(3248,\cdot)\) \(\chi_{6025}(3263,\cdot)\) \(\chi_{6025}(3812,\cdot)\) \(\chi_{6025}(4208,\cdot)\) \(\chi_{6025}(4223,\cdot)\) \(\chi_{6025}(4262,\cdot)\) \(\chi_{6025}(4453,\cdot)\) \(\chi_{6025}(5017,\cdot)\) \(\chi_{6025}(5137,\cdot)\) \(\chi_{6025}(5413,\cdot)\) \(\chi_{6025}(5428,\cdot)\) \(\chi_{6025}(5467,\cdot)\) \(\chi_{6025}(5587,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{3}{16}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{23}{80}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{77}{80}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{80})$
Fixed field: Number field defined by a degree 80 polynomial