Properties

Label 6025.57
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([20,9]))
 
pari: [g,chi] = znchar(Mod(57,6025))
 

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 \(\chi_{1205}(57,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.hb

\(\chi_{6025}(57,\cdot)\) \(\chi_{6025}(93,\cdot)\) \(\chi_{6025}(168,\cdot)\) \(\chi_{6025}(218,\cdot)\) \(\chi_{6025}(618,\cdot)\) \(\chi_{6025}(907,\cdot)\) \(\chi_{6025}(1007,\cdot)\) \(\chi_{6025}(1307,\cdot)\) \(\chi_{6025}(1343,\cdot)\) \(\chi_{6025}(1418,\cdot)\) \(\chi_{6025}(1843,\cdot)\) \(\chi_{6025}(1907,\cdot)\) \(\chi_{6025}(2143,\cdot)\) \(\chi_{6025}(2918,\cdot)\) \(\chi_{6025}(3032,\cdot)\) \(\chi_{6025}(3218,\cdot)\) \(\chi_{6025}(3257,\cdot)\) \(\chi_{6025}(3357,\cdot)\) \(\chi_{6025}(3407,\cdot)\) \(\chi_{6025}(3582,\cdot)\) \(\chi_{6025}(3632,\cdot)\) \(\chi_{6025}(3643,\cdot)\) \(\chi_{6025}(3718,\cdot)\) \(\chi_{6025}(3732,\cdot)\) \(\chi_{6025}(3957,\cdot)\) \(\chi_{6025}(4443,\cdot)\) \(\chi_{6025}(4843,\cdot)\) \(\chi_{6025}(4893,\cdot)\) \(\chi_{6025}(4968,\cdot)\) \(\chi_{6025}(5082,\cdot)\) ...

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

\((2652,2176)\) → \((i,e\left(\frac{9}{80}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{40}\right)\)\(i\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{3}{80}\right)\)
value at e.g. 2

Related number fields

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