Properties

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

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[47]
 
pari: [g,chi] = znchar(Mod(47,7623))
 

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.fz
Orbit index = 156

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 ]
 

\(\chi_{7623}(47,\cdot)\) \(\chi_{7623}(59,\cdot)\) \(\chi_{7623}(185,\cdot)\) \(\chi_{7623}(236,\cdot)\) \(\chi_{7623}(311,\cdot)\) \(\chi_{7623}(488,\cdot)\) \(\chi_{7623}(500,\cdot)\) \(\chi_{7623}(740,\cdot)\) \(\chi_{7623}(752,\cdot)\) \(\chi_{7623}(878,\cdot)\) \(\chi_{7623}(929,\cdot)\) \(\chi_{7623}(1004,\cdot)\) \(\chi_{7623}(1181,\cdot)\) \(\chi_{7623}(1193,\cdot)\) \(\chi_{7623}(1307,\cdot)\) \(\chi_{7623}(1433,\cdot)\) \(\chi_{7623}(1445,\cdot)\) \(\chi_{7623}(1571,\cdot)\) \(\chi_{7623}(1622,\cdot)\) \(\chi_{7623}(1874,\cdot)\) \(\chi_{7623}(1886,\cdot)\) \(\chi_{7623}(2000,\cdot)\) \(\chi_{7623}(2126,\cdot)\) \(\chi_{7623}(2264,\cdot)\) \(\chi_{7623}(2315,\cdot)\) \(\chi_{7623}(2390,\cdot)\) \(\chi_{7623}(2567,\cdot)\) \(\chi_{7623}(2579,\cdot)\) \(\chi_{7623}(2693,\cdot)\) \(\chi_{7623}(2819,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{6}\right),e\left(\frac{49}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{239}{330}\right)\)\(e\left(\frac{74}{165}\right)\)\(e\left(\frac{51}{55}\right)\)\(e\left(\frac{19}{110}\right)\)\(e\left(\frac{43}{66}\right)\)\(e\left(\frac{269}{330}\right)\)\(e\left(\frac{148}{165}\right)\)\(e\left(\frac{163}{165}\right)\)\(e\left(\frac{37}{330}\right)\)\(e\left(\frac{62}{165}\right)\)
value at  e.g. 2

Related number fields

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