Properties

Label 3630.29
Modulus $3630$
Conductor $1815$
Order $110$
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(3630)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([55,55,17]))
 
pari: [g,chi] = znchar(Mod(29,3630))
 

Basic properties

Modulus: \(3630\)
Conductor: \(1815\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(110\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1815}(29,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3630.bp

\(\chi_{3630}(29,\cdot)\) \(\chi_{3630}(149,\cdot)\) \(\chi_{3630}(299,\cdot)\) \(\chi_{3630}(359,\cdot)\) \(\chi_{3630}(479,\cdot)\) \(\chi_{3630}(569,\cdot)\) \(\chi_{3630}(629,\cdot)\) \(\chi_{3630}(689,\cdot)\) \(\chi_{3630}(809,\cdot)\) \(\chi_{3630}(899,\cdot)\) \(\chi_{3630}(1019,\cdot)\) \(\chi_{3630}(1139,\cdot)\) \(\chi_{3630}(1229,\cdot)\) \(\chi_{3630}(1289,\cdot)\) \(\chi_{3630}(1349,\cdot)\) \(\chi_{3630}(1469,\cdot)\) \(\chi_{3630}(1559,\cdot)\) \(\chi_{3630}(1619,\cdot)\) \(\chi_{3630}(1679,\cdot)\) \(\chi_{3630}(1799,\cdot)\) \(\chi_{3630}(1889,\cdot)\) \(\chi_{3630}(1949,\cdot)\) \(\chi_{3630}(2009,\cdot)\) \(\chi_{3630}(2129,\cdot)\) \(\chi_{3630}(2219,\cdot)\) \(\chi_{3630}(2279,\cdot)\) \(\chi_{3630}(2459,\cdot)\) \(\chi_{3630}(2549,\cdot)\) \(\chi_{3630}(2609,\cdot)\) \(\chi_{3630}(2669,\cdot)\) ...

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

\((1211,727,3511)\) → \((-1,-1,e\left(\frac{17}{110}\right))\)

Values

\(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{32}{55}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{63}{110}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{7}{55}\right)\)\(e\left(\frac{16}{55}\right)\)\(e\left(\frac{109}{110}\right)\)\(e\left(\frac{3}{55}\right)\)\(e\left(\frac{4}{11}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{55})$
Fixed field: Number field defined by a degree 110 polynomial