Properties

Label 34272.4499
Modulus $34272$
Conductor $11424$
Order $48$
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34272, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([24,42,24,40,21]))
 
Copy content pari:[g,chi] = znchar(Mod(4499,34272))
 

Basic properties

Modulus: \(34272\)
Conductor: \(11424\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(48\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{11424}(4499,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 34272.bnh

\(\chi_{34272}(2987,\cdot)\) \(\chi_{34272}(4499,\cdot)\) \(\chi_{34272}(5003,\cdot)\) \(\chi_{34272}(5939,\cdot)\) \(\chi_{34272}(8027,\cdot)\) \(\chi_{34272}(12995,\cdot)\) \(\chi_{34272}(17027,\cdot)\) \(\chi_{34272}(19547,\cdot)\) \(\chi_{34272}(20627,\cdot)\) \(\chi_{34272}(22571,\cdot)\) \(\chi_{34272}(24083,\cdot)\) \(\chi_{34272}(24587,\cdot)\) \(\chi_{34272}(27611,\cdot)\) \(\chi_{34272}(27683,\cdot)\) \(\chi_{34272}(31715,\cdot)\) \(\chi_{34272}(34235,\cdot)\)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

\((2143,29989,3809,14689,14113)\) → \((-1,e\left(\frac{7}{8}\right),-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{16}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 34272 }(4499, a) \) \(1\)\(1\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{13}{48}\right)\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{1}{16}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 34272 }(4499,a) \;\) at \(\;a = \) e.g. 2