Properties

Label 2850.17
Modulus $2850$
Conductor $1425$
Order $180$
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(180))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([90,117,100]))
 
pari: [g,chi] = znchar(Mod(17,2850))
 

Basic properties

Modulus: \(2850\)
Conductor: \(1425\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(180\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1425}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2850.cr

\(\chi_{2850}(17,\cdot)\) \(\chi_{2850}(23,\cdot)\) \(\chi_{2850}(47,\cdot)\) \(\chi_{2850}(137,\cdot)\) \(\chi_{2850}(233,\cdot)\) \(\chi_{2850}(263,\cdot)\) \(\chi_{2850}(347,\cdot)\) \(\chi_{2850}(377,\cdot)\) \(\chi_{2850}(473,\cdot)\) \(\chi_{2850}(503,\cdot)\) \(\chi_{2850}(587,\cdot)\) \(\chi_{2850}(617,\cdot)\) \(\chi_{2850}(803,\cdot)\) \(\chi_{2850}(833,\cdot)\) \(\chi_{2850}(917,\cdot)\) \(\chi_{2850}(947,\cdot)\) \(\chi_{2850}(1013,\cdot)\) \(\chi_{2850}(1073,\cdot)\) \(\chi_{2850}(1127,\cdot)\) \(\chi_{2850}(1163,\cdot)\) \(\chi_{2850}(1187,\cdot)\) \(\chi_{2850}(1277,\cdot)\) \(\chi_{2850}(1373,\cdot)\) \(\chi_{2850}(1403,\cdot)\) \(\chi_{2850}(1487,\cdot)\) \(\chi_{2850}(1517,\cdot)\) \(\chi_{2850}(1583,\cdot)\) \(\chi_{2850}(1613,\cdot)\) \(\chi_{2850}(1697,\cdot)\) \(\chi_{2850}(1727,\cdot)\) ...

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: $\Q(\zeta_{180})$
Fixed field: Number field defined by a degree 180 polynomial (not computed)

Values on generators

\((1901,1027,1351)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{5}{9}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{23}{180}\right)\)\(e\left(\frac{91}{180}\right)\)\(e\left(\frac{137}{180}\right)\)\(e\left(\frac{11}{45}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{29}{90}\right)\)\(e\left(\frac{23}{36}\right)\)
value at e.g. 2