Properties

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

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[1942]
 
pari: [g,chi] = znchar(Mod(1942,7623))
 

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.fe
Orbit index = 135

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 ]
 

\(\chi_{7623}(52,\cdot)\) \(\chi_{7623}(178,\cdot)\) \(\chi_{7623}(292,\cdot)\) \(\chi_{7623}(304,\cdot)\) \(\chi_{7623}(556,\cdot)\) \(\chi_{7623}(607,\cdot)\) \(\chi_{7623}(733,\cdot)\) \(\chi_{7623}(745,\cdot)\) \(\chi_{7623}(871,\cdot)\) \(\chi_{7623}(985,\cdot)\) \(\chi_{7623}(997,\cdot)\) \(\chi_{7623}(1174,\cdot)\) \(\chi_{7623}(1249,\cdot)\) \(\chi_{7623}(1300,\cdot)\) \(\chi_{7623}(1426,\cdot)\) \(\chi_{7623}(1438,\cdot)\) \(\chi_{7623}(1678,\cdot)\) \(\chi_{7623}(1690,\cdot)\) \(\chi_{7623}(1867,\cdot)\) \(\chi_{7623}(1942,\cdot)\) \(\chi_{7623}(1993,\cdot)\) \(\chi_{7623}(2119,\cdot)\) \(\chi_{7623}(2131,\cdot)\) \(\chi_{7623}(2257,\cdot)\) \(\chi_{7623}(2371,\cdot)\) \(\chi_{7623}(2383,\cdot)\) \(\chi_{7623}(2560,\cdot)\) \(\chi_{7623}(2686,\cdot)\) \(\chi_{7623}(2812,\cdot)\) \(\chi_{7623}(2824,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{89}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{89}{110}\right)\)\(e\left(\frac{34}{55}\right)\)\(e\left(\frac{13}{330}\right)\)\(e\left(\frac{47}{110}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{91}{165}\right)\)\(e\left(\frac{13}{55}\right)\)\(e\left(\frac{134}{165}\right)\)\(e\left(\frac{163}{165}\right)\)\(e\left(\frac{217}{330}\right)\)
value at  e.g. 2

Related number fields

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