Properties

Label 3549.211
Modulus $3549$
Conductor $169$
Order $39$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3549, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,38]))
 
pari: [g,chi] = znchar(Mod(211,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(42,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3549.cr

\(\chi_{3549}(211,\cdot)\) \(\chi_{3549}(295,\cdot)\) \(\chi_{3549}(568,\cdot)\) \(\chi_{3549}(757,\cdot)\) \(\chi_{3549}(841,\cdot)\) \(\chi_{3549}(1030,\cdot)\) \(\chi_{3549}(1114,\cdot)\) \(\chi_{3549}(1303,\cdot)\) \(\chi_{3549}(1387,\cdot)\) \(\chi_{3549}(1576,\cdot)\) \(\chi_{3549}(1660,\cdot)\) \(\chi_{3549}(1849,\cdot)\) \(\chi_{3549}(1933,\cdot)\) \(\chi_{3549}(2122,\cdot)\) \(\chi_{3549}(2206,\cdot)\) \(\chi_{3549}(2395,\cdot)\) \(\chi_{3549}(2479,\cdot)\) \(\chi_{3549}(2668,\cdot)\) \(\chi_{3549}(2752,\cdot)\) \(\chi_{3549}(2941,\cdot)\) \(\chi_{3549}(3025,\cdot)\) \(\chi_{3549}(3214,\cdot)\) \(\chi_{3549}(3298,\cdot)\) \(\chi_{3549}(3487,\cdot)\)

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: $\Q(\zeta_{39})$
Fixed field: 39.39.27027636582498189040621249864144468324898507852136260989871841246090732111847218889.1

Values on generators

\((1184,1522,3382)\) → \((1,1,e\left(\frac{19}{39}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{19}{39}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{34}{39}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{37}{39}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{14}{39}\right)\)
value at e.g. 2