Properties

Label 2304.41
Modulus $2304$
Conductor $1152$
Order $96$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2304, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,93,80]))
 
pari: [g,chi] = znchar(Mod(41,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(1152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1152}(77,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bx

\(\chi_{2304}(41,\cdot)\) \(\chi_{2304}(137,\cdot)\) \(\chi_{2304}(185,\cdot)\) \(\chi_{2304}(281,\cdot)\) \(\chi_{2304}(329,\cdot)\) \(\chi_{2304}(425,\cdot)\) \(\chi_{2304}(473,\cdot)\) \(\chi_{2304}(569,\cdot)\) \(\chi_{2304}(617,\cdot)\) \(\chi_{2304}(713,\cdot)\) \(\chi_{2304}(761,\cdot)\) \(\chi_{2304}(857,\cdot)\) \(\chi_{2304}(905,\cdot)\) \(\chi_{2304}(1001,\cdot)\) \(\chi_{2304}(1049,\cdot)\) \(\chi_{2304}(1145,\cdot)\) \(\chi_{2304}(1193,\cdot)\) \(\chi_{2304}(1289,\cdot)\) \(\chi_{2304}(1337,\cdot)\) \(\chi_{2304}(1433,\cdot)\) \(\chi_{2304}(1481,\cdot)\) \(\chi_{2304}(1577,\cdot)\) \(\chi_{2304}(1625,\cdot)\) \(\chi_{2304}(1721,\cdot)\) \(\chi_{2304}(1769,\cdot)\) \(\chi_{2304}(1865,\cdot)\) \(\chi_{2304}(1913,\cdot)\) \(\chi_{2304}(2009,\cdot)\) \(\chi_{2304}(2057,\cdot)\) \(\chi_{2304}(2153,\cdot)\) ...

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: $\Q(\zeta_{96})$
Fixed field: Number field defined by a degree 96 polynomial

Values on generators

\((1279,2053,1793)\) → \((1,e\left(\frac{31}{32}\right),e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{13}{96}\right)\)\(e\left(\frac{1}{48}\right)\)\(e\left(\frac{17}{96}\right)\)\(e\left(\frac{19}{96}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{32}\right)\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{13}{48}\right)\)\(e\left(\frac{95}{96}\right)\)\(e\left(\frac{5}{12}\right)\)
value at e.g. 2