Properties

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

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[5609]
 
pari: [g,chi] = znchar(Mod(5609,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.em
Orbit index = 117

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 ]
 

\(\chi_{7623}(32,\cdot)\) \(\chi_{7623}(65,\cdot)\) \(\chi_{7623}(758,\cdot)\) \(\chi_{7623}(1418,\cdot)\) \(\chi_{7623}(2111,\cdot)\) \(\chi_{7623}(2144,\cdot)\) \(\chi_{7623}(2804,\cdot)\) \(\chi_{7623}(2837,\cdot)\) \(\chi_{7623}(3497,\cdot)\) \(\chi_{7623}(3530,\cdot)\) \(\chi_{7623}(4190,\cdot)\) \(\chi_{7623}(4223,\cdot)\) \(\chi_{7623}(4883,\cdot)\) \(\chi_{7623}(4916,\cdot)\) \(\chi_{7623}(5576,\cdot)\) \(\chi_{7623}(5609,\cdot)\) \(\chi_{7623}(6269,\cdot)\) \(\chi_{7623}(6302,\cdot)\) \(\chi_{7623}(6962,\cdot)\) \(\chi_{7623}(6995,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{5}{22}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{29}{66}\right)\)
value at  e.g. 2

Related number fields

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