Properties

Label 2304.35
Modulus $2304$
Conductor $768$
Order $64$
Real no
Primitive no
Minimal yes
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([32,11,32]))
 
pari: [g,chi] = znchar(Mod(35,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(768\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{768}(35,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bu

\(\chi_{2304}(35,\cdot)\) \(\chi_{2304}(107,\cdot)\) \(\chi_{2304}(179,\cdot)\) \(\chi_{2304}(251,\cdot)\) \(\chi_{2304}(323,\cdot)\) \(\chi_{2304}(395,\cdot)\) \(\chi_{2304}(467,\cdot)\) \(\chi_{2304}(539,\cdot)\) \(\chi_{2304}(611,\cdot)\) \(\chi_{2304}(683,\cdot)\) \(\chi_{2304}(755,\cdot)\) \(\chi_{2304}(827,\cdot)\) \(\chi_{2304}(899,\cdot)\) \(\chi_{2304}(971,\cdot)\) \(\chi_{2304}(1043,\cdot)\) \(\chi_{2304}(1115,\cdot)\) \(\chi_{2304}(1187,\cdot)\) \(\chi_{2304}(1259,\cdot)\) \(\chi_{2304}(1331,\cdot)\) \(\chi_{2304}(1403,\cdot)\) \(\chi_{2304}(1475,\cdot)\) \(\chi_{2304}(1547,\cdot)\) \(\chi_{2304}(1619,\cdot)\) \(\chi_{2304}(1691,\cdot)\) \(\chi_{2304}(1763,\cdot)\) \(\chi_{2304}(1835,\cdot)\) \(\chi_{2304}(1907,\cdot)\) \(\chi_{2304}(1979,\cdot)\) \(\chi_{2304}(2051,\cdot)\) \(\chi_{2304}(2123,\cdot)\) ...

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

\((1279,2053,1793)\) → \((-1,e\left(\frac{11}{64}\right),-1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{43}{64}\right)\)\(e\left(\frac{7}{32}\right)\)\(e\left(\frac{39}{64}\right)\)\(e\left(\frac{5}{64}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{29}{64}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{11}{32}\right)\)\(e\left(\frac{41}{64}\right)\)\(e\left(\frac{7}{8}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{64})$
Fixed field: Number field defined by a degree 64 polynomial