Properties

Label 1815.29
Modulus $1815$
Conductor $1815$
Order $110$
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(110))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([55,55,17]))
 
pari: [g,chi] = znchar(Mod(29,1815))
 

Basic properties

Modulus: \(1815\)
Conductor: \(1815\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(110\)
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.bn

\(\chi_{1815}(29,\cdot)\) \(\chi_{1815}(74,\cdot)\) \(\chi_{1815}(134,\cdot)\) \(\chi_{1815}(149,\cdot)\) \(\chi_{1815}(194,\cdot)\) \(\chi_{1815}(299,\cdot)\) \(\chi_{1815}(314,\cdot)\) \(\chi_{1815}(359,\cdot)\) \(\chi_{1815}(404,\cdot)\) \(\chi_{1815}(464,\cdot)\) \(\chi_{1815}(479,\cdot)\) \(\chi_{1815}(569,\cdot)\) \(\chi_{1815}(629,\cdot)\) \(\chi_{1815}(644,\cdot)\) \(\chi_{1815}(689,\cdot)\) \(\chi_{1815}(734,\cdot)\) \(\chi_{1815}(794,\cdot)\) \(\chi_{1815}(809,\cdot)\) \(\chi_{1815}(854,\cdot)\) \(\chi_{1815}(899,\cdot)\) \(\chi_{1815}(974,\cdot)\) \(\chi_{1815}(1019,\cdot)\) \(\chi_{1815}(1064,\cdot)\) \(\chi_{1815}(1124,\cdot)\) \(\chi_{1815}(1139,\cdot)\) \(\chi_{1815}(1184,\cdot)\) \(\chi_{1815}(1229,\cdot)\) \(\chi_{1815}(1289,\cdot)\) \(\chi_{1815}(1349,\cdot)\) \(\chi_{1815}(1394,\cdot)\) ...

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

\((1211,727,1696)\) → \((-1,-1,e\left(\frac{17}{110}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(13\)\(14\)\(16\)\(17\)\(19\)\(23\)
\(1\)\(1\)\(e\left(\frac{17}{110}\right)\)\(e\left(\frac{17}{55}\right)\)\(e\left(\frac{32}{55}\right)\)\(e\left(\frac{51}{110}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{81}{110}\right)\)\(e\left(\frac{34}{55}\right)\)\(e\left(\frac{63}{110}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{9}{11}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{55})$
Fixed field: Number field defined by a degree 110 polynomial (not computed)