Properties

Label 1152.5
Modulus $1152$
Conductor $1152$
Order $96$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1152, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,80]))
 
pari: [g,chi] = znchar(Mod(5,1152))
 

Basic properties

Modulus: \(1152\)
Conductor: \(1152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1152.bt

\(\chi_{1152}(5,\cdot)\) \(\chi_{1152}(29,\cdot)\) \(\chi_{1152}(77,\cdot)\) \(\chi_{1152}(101,\cdot)\) \(\chi_{1152}(149,\cdot)\) \(\chi_{1152}(173,\cdot)\) \(\chi_{1152}(221,\cdot)\) \(\chi_{1152}(245,\cdot)\) \(\chi_{1152}(293,\cdot)\) \(\chi_{1152}(317,\cdot)\) \(\chi_{1152}(365,\cdot)\) \(\chi_{1152}(389,\cdot)\) \(\chi_{1152}(437,\cdot)\) \(\chi_{1152}(461,\cdot)\) \(\chi_{1152}(509,\cdot)\) \(\chi_{1152}(533,\cdot)\) \(\chi_{1152}(581,\cdot)\) \(\chi_{1152}(605,\cdot)\) \(\chi_{1152}(653,\cdot)\) \(\chi_{1152}(677,\cdot)\) \(\chi_{1152}(725,\cdot)\) \(\chi_{1152}(749,\cdot)\) \(\chi_{1152}(797,\cdot)\) \(\chi_{1152}(821,\cdot)\) \(\chi_{1152}(869,\cdot)\) \(\chi_{1152}(893,\cdot)\) \(\chi_{1152}(941,\cdot)\) \(\chi_{1152}(965,\cdot)\) \(\chi_{1152}(1013,\cdot)\) \(\chi_{1152}(1037,\cdot)\) ...

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

\((127,901,641)\) → \((1,e\left(\frac{1}{32}\right),e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{19}{96}\right)\)\(e\left(\frac{31}{48}\right)\)\(e\left(\frac{47}{96}\right)\)\(e\left(\frac{13}{96}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{19}{48}\right)\)\(e\left(\frac{65}{96}\right)\)\(e\left(\frac{11}{12}\right)\)
value at e.g. 2