Properties

Label 1148.69
Modulus $1148$
Conductor $287$
Order $40$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1148, base_ring=CyclotomicField(40))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,20,11]))
 
pari: [g,chi] = znchar(Mod(69,1148))
 

Basic properties

Modulus: \(1148\)
Conductor: \(287\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{287}(69,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1148.cc

\(\chi_{1148}(13,\cdot)\) \(\chi_{1148}(69,\cdot)\) \(\chi_{1148}(97,\cdot)\) \(\chi_{1148}(153,\cdot)\) \(\chi_{1148}(181,\cdot)\) \(\chi_{1148}(265,\cdot)\) \(\chi_{1148}(293,\cdot)\) \(\chi_{1148}(321,\cdot)\) \(\chi_{1148}(545,\cdot)\) \(\chi_{1148}(685,\cdot)\) \(\chi_{1148}(909,\cdot)\) \(\chi_{1148}(937,\cdot)\) \(\chi_{1148}(965,\cdot)\) \(\chi_{1148}(1049,\cdot)\) \(\chi_{1148}(1077,\cdot)\) \(\chi_{1148}(1133,\cdot)\)

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: \(\Q(\zeta_{40})\)
Fixed field: 40.40.63172957949423116502957480067191906200305068755882825968063357506461803384975161.1

Values on generators

\((575,493,785)\) → \((1,-1,e\left(\frac{11}{40}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(1\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{11}{20}\right)\)\(i\)\(e\left(\frac{33}{40}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{10}\right)\)
value at e.g. 2