Properties

Label 6025.676
Modulus $6025$
Conductor $241$
Order $40$
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([0,39]))
 
pari: [g,chi] = znchar(Mod(676,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(241\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{241}(194,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.es

\(\chi_{6025}(676,\cdot)\) \(\chi_{6025}(1126,\cdot)\) \(\chi_{6025}(1451,\cdot)\) \(\chi_{6025}(1626,\cdot)\) \(\chi_{6025}(1901,\cdot)\) \(\chi_{6025}(1976,\cdot)\) \(\chi_{6025}(2451,\cdot)\) \(\chi_{6025}(2526,\cdot)\) \(\chi_{6025}(2776,\cdot)\) \(\chi_{6025}(2851,\cdot)\) \(\chi_{6025}(3326,\cdot)\) \(\chi_{6025}(3401,\cdot)\) \(\chi_{6025}(3676,\cdot)\) \(\chi_{6025}(3851,\cdot)\) \(\chi_{6025}(4176,\cdot)\) \(\chi_{6025}(4626,\cdot)\)

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

\((2652,2176)\) → \((1,e\left(\frac{39}{40}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(i\)\(e\left(\frac{9}{20}\right)\)\(-1\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{39}{40}\right)\)\(-i\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{33}{40}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: 40.40.791889638416655580350456569351034349494321492589146381070272539583828111934638205267822786961.1