Properties

Conductor 7623
Order 330
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 7623.fw

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[13]
 
pari: [g,chi] = znchar(Mod(13,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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.fw
Orbit index = 153

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 ]
 

\(\chi_{7623}(13,\cdot)\) \(\chi_{7623}(139,\cdot)\) \(\chi_{7623}(160,\cdot)\) \(\chi_{7623}(349,\cdot)\) \(\chi_{7623}(391,\cdot)\) \(\chi_{7623}(580,\cdot)\) \(\chi_{7623}(601,\cdot)\) \(\chi_{7623}(706,\cdot)\) \(\chi_{7623}(832,\cdot)\) \(\chi_{7623}(853,\cdot)\) \(\chi_{7623}(1042,\cdot)\) \(\chi_{7623}(1084,\cdot)\) \(\chi_{7623}(1168,\cdot)\) \(\chi_{7623}(1273,\cdot)\) \(\chi_{7623}(1294,\cdot)\) \(\chi_{7623}(1399,\cdot)\) \(\chi_{7623}(1525,\cdot)\) \(\chi_{7623}(1735,\cdot)\) \(\chi_{7623}(1777,\cdot)\) \(\chi_{7623}(1861,\cdot)\) \(\chi_{7623}(1966,\cdot)\) \(\chi_{7623}(1987,\cdot)\) \(\chi_{7623}(2092,\cdot)\) \(\chi_{7623}(2239,\cdot)\) \(\chi_{7623}(2428,\cdot)\) \(\chi_{7623}(2470,\cdot)\) \(\chi_{7623}(2554,\cdot)\) \(\chi_{7623}(2680,\cdot)\) \(\chi_{7623}(2785,\cdot)\) \(\chi_{7623}(2911,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{101}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{83}{330}\right)\)\(e\left(\frac{83}{165}\right)\)\(e\left(\frac{37}{330}\right)\)\(e\left(\frac{83}{110}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{149}{165}\right)\)\(e\left(\frac{1}{165}\right)\)\(e\left(\frac{27}{55}\right)\)\(e\left(\frac{39}{55}\right)\)\(e\left(\frac{203}{330}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)