Properties

Label 3024.43
Modulus $3024$
Conductor $432$
Order $36$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3024, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,9,8,0]))
 
pari: [g,chi] = znchar(Mod(43,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(432\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{432}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.gw

\(\chi_{3024}(43,\cdot)\) \(\chi_{3024}(211,\cdot)\) \(\chi_{3024}(547,\cdot)\) \(\chi_{3024}(715,\cdot)\) \(\chi_{3024}(1051,\cdot)\) \(\chi_{3024}(1219,\cdot)\) \(\chi_{3024}(1555,\cdot)\) \(\chi_{3024}(1723,\cdot)\) \(\chi_{3024}(2059,\cdot)\) \(\chi_{3024}(2227,\cdot)\) \(\chi_{3024}(2563,\cdot)\) \(\chi_{3024}(2731,\cdot)\)

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

\((1135,757,785,2593)\) → \((-1,i,e\left(\frac{2}{9}\right),1)\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{13}{36}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{35}{36}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{7}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.614667125325361522818798575155151578949632894783197825857500612833312768.1