Properties

Label 1815.23
Modulus $1815$
Conductor $1815$
Order $44$
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(1815, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,33,28]))
 
pari: [g,chi] = znchar(Mod(23,1815))
 

Basic properties

Modulus: \(1815\)
Conductor: \(1815\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
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 1815.bh

\(\chi_{1815}(23,\cdot)\) \(\chi_{1815}(188,\cdot)\) \(\chi_{1815}(287,\cdot)\) \(\chi_{1815}(353,\cdot)\) \(\chi_{1815}(452,\cdot)\) \(\chi_{1815}(518,\cdot)\) \(\chi_{1815}(617,\cdot)\) \(\chi_{1815}(683,\cdot)\) \(\chi_{1815}(782,\cdot)\) \(\chi_{1815}(947,\cdot)\) \(\chi_{1815}(1013,\cdot)\) \(\chi_{1815}(1112,\cdot)\) \(\chi_{1815}(1178,\cdot)\) \(\chi_{1815}(1277,\cdot)\) \(\chi_{1815}(1343,\cdot)\) \(\chi_{1815}(1442,\cdot)\) \(\chi_{1815}(1508,\cdot)\) \(\chi_{1815}(1607,\cdot)\) \(\chi_{1815}(1673,\cdot)\) \(\chi_{1815}(1772,\cdot)\)

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

\((1211,727,1696)\) → \((-1,-i,e\left(\frac{7}{11}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(13\)\(14\)\(16\)\(17\)\(19\)\(23\)
\(1\)\(1\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{13}{44}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial