Properties

Label 2850.41
Modulus $2850$
Conductor $1425$
Order $90$
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(90))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([45,18,65]))
 
pari: [g,chi] = znchar(Mod(41,2850))
 

Basic properties

Modulus: \(2850\)
Conductor: \(1425\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(90\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1425}(41,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2850.cj

\(\chi_{2850}(41,\cdot)\) \(\chi_{2850}(71,\cdot)\) \(\chi_{2850}(281,\cdot)\) \(\chi_{2850}(371,\cdot)\) \(\chi_{2850}(431,\cdot)\) \(\chi_{2850}(611,\cdot)\) \(\chi_{2850}(641,\cdot)\) \(\chi_{2850}(941,\cdot)\) \(\chi_{2850}(971,\cdot)\) \(\chi_{2850}(1181,\cdot)\) \(\chi_{2850}(1211,\cdot)\) \(\chi_{2850}(1421,\cdot)\) \(\chi_{2850}(1511,\cdot)\) \(\chi_{2850}(1541,\cdot)\) \(\chi_{2850}(1571,\cdot)\) \(\chi_{2850}(1781,\cdot)\) \(\chi_{2850}(1991,\cdot)\) \(\chi_{2850}(2081,\cdot)\) \(\chi_{2850}(2111,\cdot)\) \(\chi_{2850}(2141,\cdot)\) \(\chi_{2850}(2321,\cdot)\) \(\chi_{2850}(2561,\cdot)\) \(\chi_{2850}(2681,\cdot)\) \(\chi_{2850}(2711,\cdot)\)

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: $\Q(\zeta_{45})$
Fixed field: Number field defined by a degree 90 polynomial

Values on generators

\((1901,1027,1351)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{13}{18}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{37}{90}\right)\)\(e\left(\frac{29}{90}\right)\)\(e\left(\frac{13}{90}\right)\)\(e\left(\frac{8}{45}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{5}{9}\right)\)
value at e.g. 2