Properties

Label 2850.619
Modulus $2850$
Conductor $475$
Order $30$
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(2850, base_ring=CyclotomicField(30))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,27,20]))
 
pari: [g,chi] = znchar(Mod(619,2850))
 

Basic properties

Modulus: \(2850\)
Conductor: \(475\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{475}(144,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2850.bt

\(\chi_{2850}(619,\cdot)\) \(\chi_{2850}(919,\cdot)\) \(\chi_{2850}(1189,\cdot)\) \(\chi_{2850}(1489,\cdot)\) \(\chi_{2850}(1759,\cdot)\) \(\chi_{2850}(2059,\cdot)\) \(\chi_{2850}(2329,\cdot)\) \(\chi_{2850}(2629,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: 30.30.16693301611046410834296161329604046841268427670001983642578125.1

Values on generators

\((1901,1027,1351)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(-1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2