Properties

Label 6025.42
Modulus $6025$
Conductor $6025$
Order $240$
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([156,133]))
 
pari: [g,chi] = znchar(Mod(42,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.jd

\(\chi_{6025}(42,\cdot)\) \(\chi_{6025}(163,\cdot)\) \(\chi_{6025}(173,\cdot)\) \(\chi_{6025}(228,\cdot)\) \(\chi_{6025}(292,\cdot)\) \(\chi_{6025}(408,\cdot)\) \(\chi_{6025}(412,\cdot)\) \(\chi_{6025}(413,\cdot)\) \(\chi_{6025}(528,\cdot)\) \(\chi_{6025}(592,\cdot)\) \(\chi_{6025}(637,\cdot)\) \(\chi_{6025}(688,\cdot)\) \(\chi_{6025}(762,\cdot)\) \(\chi_{6025}(852,\cdot)\) \(\chi_{6025}(872,\cdot)\) \(\chi_{6025}(902,\cdot)\) \(\chi_{6025}(1153,\cdot)\) \(\chi_{6025}(1242,\cdot)\) \(\chi_{6025}(1273,\cdot)\) \(\chi_{6025}(1297,\cdot)\) \(\chi_{6025}(1578,\cdot)\) \(\chi_{6025}(1673,\cdot)\) \(\chi_{6025}(1833,\cdot)\) \(\chi_{6025}(1963,\cdot)\) \(\chi_{6025}(1983,\cdot)\) \(\chi_{6025}(2238,\cdot)\) \(\chi_{6025}(2278,\cdot)\) \(\chi_{6025}(2488,\cdot)\) \(\chi_{6025}(2547,\cdot)\) \(\chi_{6025}(2612,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{133}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{113}{120}\right)\)\(e\left(\frac{49}{120}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{193}{240}\right)\)\(e\left(\frac{33}{40}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{61}{240}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{19}{48}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial