Properties

Conductor 847
Order 22
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.cg

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(7623)
 
sage: chi = H[307]
 
pari: [g,chi] = znchar(Mod(307,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 22
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.cg
Orbit index = 59

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{7623}(307,\cdot)\) \(\chi_{7623}(1000,\cdot)\) \(\chi_{7623}(2386,\cdot)\) \(\chi_{7623}(3079,\cdot)\) \(\chi_{7623}(3772,\cdot)\) \(\chi_{7623}(4465,\cdot)\) \(\chi_{7623}(5158,\cdot)\) \(\chi_{7623}(5851,\cdot)\) \(\chi_{7623}(6544,\cdot)\) \(\chi_{7623}(7237,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((1,-1,e\left(\frac{13}{22}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{9}{22}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{11})\)