Properties

Label 6025.43
Modulus $6025$
Conductor $1205$
Order $80$
Real no
Primitive no
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([60,73]))
 
pari: [g,chi] = znchar(Mod(43,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(80\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.ha

\(\chi_{6025}(43,\cdot)\) \(\chi_{6025}(343,\cdot)\) \(\chi_{6025}(943,\cdot)\) \(\chi_{6025}(1057,\cdot)\) \(\chi_{6025}(1132,\cdot)\) \(\chi_{6025}(1182,\cdot)\) \(\chi_{6025}(1582,\cdot)\) \(\chi_{6025}(2068,\cdot)\) \(\chi_{6025}(2293,\cdot)\) \(\chi_{6025}(2307,\cdot)\) \(\chi_{6025}(2382,\cdot)\) \(\chi_{6025}(2393,\cdot)\) \(\chi_{6025}(2443,\cdot)\) \(\chi_{6025}(2618,\cdot)\) \(\chi_{6025}(2668,\cdot)\) \(\chi_{6025}(2768,\cdot)\) \(\chi_{6025}(2807,\cdot)\) \(\chi_{6025}(2993,\cdot)\) \(\chi_{6025}(3107,\cdot)\) \(\chi_{6025}(3882,\cdot)\) \(\chi_{6025}(4118,\cdot)\) \(\chi_{6025}(4182,\cdot)\) \(\chi_{6025}(4607,\cdot)\) \(\chi_{6025}(4682,\cdot)\) \(\chi_{6025}(4718,\cdot)\) \(\chi_{6025}(5018,\cdot)\) \(\chi_{6025}(5118,\cdot)\) \(\chi_{6025}(5407,\cdot)\) \(\chi_{6025}(5807,\cdot)\) \(\chi_{6025}(5857,\cdot)\) ...

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

\((2652,2176)\) → \((-i,e\left(\frac{73}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{13}{40}\right)\)\(i\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{53}{80}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{11}{80}\right)\)
value at e.g. 2

Related number fields

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