Properties

Label 1815.43
Modulus $1815$
Conductor $605$
Order $44$
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(1815, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,33,10]))
 
pari: [g,chi] = znchar(Mod(43,1815))
 

Basic properties

Modulus: \(1815\)
Conductor: \(605\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{605}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1815.bi

\(\chi_{1815}(43,\cdot)\) \(\chi_{1815}(142,\cdot)\) \(\chi_{1815}(208,\cdot)\) \(\chi_{1815}(307,\cdot)\) \(\chi_{1815}(373,\cdot)\) \(\chi_{1815}(472,\cdot)\) \(\chi_{1815}(538,\cdot)\) \(\chi_{1815}(637,\cdot)\) \(\chi_{1815}(703,\cdot)\) \(\chi_{1815}(802,\cdot)\) \(\chi_{1815}(868,\cdot)\) \(\chi_{1815}(1033,\cdot)\) \(\chi_{1815}(1132,\cdot)\) \(\chi_{1815}(1198,\cdot)\) \(\chi_{1815}(1297,\cdot)\) \(\chi_{1815}(1363,\cdot)\) \(\chi_{1815}(1462,\cdot)\) \(\chi_{1815}(1528,\cdot)\) \(\chi_{1815}(1627,\cdot)\) \(\chi_{1815}(1792,\cdot)\)

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

\((1211,727,1696)\) → \((1,-i,e\left(\frac{5}{22}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(13\)\(14\)\(16\)\(17\)\(19\)\(23\)
\(1\)\(1\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{7}{44}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.2885428559557085084648615903962269104974580506944665166312236845353556846511909399754484184086322784423828125.1