Properties

Conductor 1089
Order 66
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.eh

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[6665]
 
pari: [g,chi] = znchar(Mod(6665,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1089
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 66
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.eh
Orbit index = 112

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 ]
 

\(\chi_{7623}(428,\cdot)\) \(\chi_{7623}(659,\cdot)\) \(\chi_{7623}(1121,\cdot)\) \(\chi_{7623}(1352,\cdot)\) \(\chi_{7623}(2045,\cdot)\) \(\chi_{7623}(2507,\cdot)\) \(\chi_{7623}(2738,\cdot)\) \(\chi_{7623}(3200,\cdot)\) \(\chi_{7623}(3431,\cdot)\) \(\chi_{7623}(3893,\cdot)\) \(\chi_{7623}(4124,\cdot)\) \(\chi_{7623}(4586,\cdot)\) \(\chi_{7623}(4817,\cdot)\) \(\chi_{7623}(5279,\cdot)\) \(\chi_{7623}(5510,\cdot)\) \(\chi_{7623}(5972,\cdot)\) \(\chi_{7623}(6203,\cdot)\) \(\chi_{7623}(6665,\cdot)\) \(\chi_{7623}(7358,\cdot)\) \(\chi_{7623}(7589,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),1,e\left(\frac{15}{22}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{43}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)