Properties

Conductor 1617
Order 210
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.ci

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(3234)
 
sage: chi = H[95]
 
pari: [g,chi] = znchar(Mod(95,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1617
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
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 = 3234.ci
Orbit index = 61

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 ]
 

\(\chi_{3234}(95,\cdot)\) \(\chi_{3234}(107,\cdot)\) \(\chi_{3234}(149,\cdot)\) \(\chi_{3234}(233,\cdot)\) \(\chi_{3234}(305,\cdot)\) \(\chi_{3234}(347,\cdot)\) \(\chi_{3234}(359,\cdot)\) \(\chi_{3234}(431,\cdot)\) \(\chi_{3234}(611,\cdot)\) \(\chi_{3234}(695,\cdot)\) \(\chi_{3234}(767,\cdot)\) \(\chi_{3234}(809,\cdot)\) \(\chi_{3234}(821,\cdot)\) \(\chi_{3234}(893,\cdot)\) \(\chi_{3234}(1019,\cdot)\) \(\chi_{3234}(1031,\cdot)\) \(\chi_{3234}(1073,\cdot)\) \(\chi_{3234}(1229,\cdot)\) \(\chi_{3234}(1271,\cdot)\) \(\chi_{3234}(1283,\cdot)\) \(\chi_{3234}(1355,\cdot)\) \(\chi_{3234}(1481,\cdot)\) \(\chi_{3234}(1493,\cdot)\) \(\chi_{3234}(1535,\cdot)\) \(\chi_{3234}(1619,\cdot)\) \(\chi_{3234}(1691,\cdot)\) \(\chi_{3234}(1817,\cdot)\) \(\chi_{3234}(1943,\cdot)\) \(\chi_{3234}(1955,\cdot)\) \(\chi_{3234}(1997,\cdot)\) ...

Values on generators

\((1079,199,2059)\) → \((-1,e\left(\frac{11}{21}\right),e\left(\frac{7}{10}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{103}{210}\right)\)\(e\left(\frac{69}{70}\right)\)\(e\left(\frac{94}{105}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{103}{105}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{17}{105}\right)\)\(e\left(\frac{16}{35}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)