Properties

Label 3150.2833
Modulus $3150$
Conductor $1575$
Order $60$
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(3150)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([40,9,50]))
 
pari: [g,chi] = znchar(Mod(2833,3150))
 

Basic properties

Modulus: \(3150\)
Conductor: \(1575\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1575}(1258,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3150.eb

\(\chi_{3150}(187,\cdot)\) \(\chi_{3150}(283,\cdot)\) \(\chi_{3150}(313,\cdot)\) \(\chi_{3150}(787,\cdot)\) \(\chi_{3150}(817,\cdot)\) \(\chi_{3150}(913,\cdot)\) \(\chi_{3150}(1417,\cdot)\) \(\chi_{3150}(1447,\cdot)\) \(\chi_{3150}(1573,\cdot)\) \(\chi_{3150}(2047,\cdot)\) \(\chi_{3150}(2077,\cdot)\) \(\chi_{3150}(2173,\cdot)\) \(\chi_{3150}(2203,\cdot)\) \(\chi_{3150}(2677,\cdot)\) \(\chi_{3150}(2803,\cdot)\) \(\chi_{3150}(2833,\cdot)\)

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

\((2801,127,451)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{20}\right),e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{11}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial