Properties

Label 2304.25
Modulus $2304$
Conductor $1152$
Order $96$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2304)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,64]))
 
pari: [g,chi] = znchar(Mod(25,2304))
 

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 \(\chi_{1152}(133,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bz

\(\chi_{2304}(25,\cdot)\) \(\chi_{2304}(121,\cdot)\) \(\chi_{2304}(169,\cdot)\) \(\chi_{2304}(265,\cdot)\) \(\chi_{2304}(313,\cdot)\) \(\chi_{2304}(409,\cdot)\) \(\chi_{2304}(457,\cdot)\) \(\chi_{2304}(553,\cdot)\) \(\chi_{2304}(601,\cdot)\) \(\chi_{2304}(697,\cdot)\) \(\chi_{2304}(745,\cdot)\) \(\chi_{2304}(841,\cdot)\) \(\chi_{2304}(889,\cdot)\) \(\chi_{2304}(985,\cdot)\) \(\chi_{2304}(1033,\cdot)\) \(\chi_{2304}(1129,\cdot)\) \(\chi_{2304}(1177,\cdot)\) \(\chi_{2304}(1273,\cdot)\) \(\chi_{2304}(1321,\cdot)\) \(\chi_{2304}(1417,\cdot)\) \(\chi_{2304}(1465,\cdot)\) \(\chi_{2304}(1561,\cdot)\) \(\chi_{2304}(1609,\cdot)\) \(\chi_{2304}(1705,\cdot)\) \(\chi_{2304}(1753,\cdot)\) \(\chi_{2304}(1849,\cdot)\) \(\chi_{2304}(1897,\cdot)\) \(\chi_{2304}(1993,\cdot)\) \(\chi_{2304}(2041,\cdot)\) \(\chi_{2304}(2137,\cdot)\) ...

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

\((1279,2053,1793)\) → \((1,e\left(\frac{1}{32}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{35}{96}\right)\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{31}{96}\right)\)\(e\left(\frac{77}{96}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{49}{96}\right)\)\(e\left(\frac{7}{12}\right)\)
value at e.g. 2

Related number fields

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