Properties

Conductor 539
Order 105
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.ce

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[25]
 
pari: [g,chi] = znchar(Mod(25,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 539
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 105
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.ce
Orbit index = 57

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 ]
 

\(\chi_{3234}(25,\cdot)\) \(\chi_{3234}(37,\cdot)\) \(\chi_{3234}(163,\cdot)\) \(\chi_{3234}(235,\cdot)\) \(\chi_{3234}(247,\cdot)\) \(\chi_{3234}(289,\cdot)\) \(\chi_{3234}(445,\cdot)\) \(\chi_{3234}(487,\cdot)\) \(\chi_{3234}(499,\cdot)\) \(\chi_{3234}(625,\cdot)\) \(\chi_{3234}(697,\cdot)\) \(\chi_{3234}(709,\cdot)\) \(\chi_{3234}(751,\cdot)\) \(\chi_{3234}(823,\cdot)\) \(\chi_{3234}(907,\cdot)\) \(\chi_{3234}(1087,\cdot)\) \(\chi_{3234}(1159,\cdot)\) \(\chi_{3234}(1171,\cdot)\) \(\chi_{3234}(1213,\cdot)\) \(\chi_{3234}(1285,\cdot)\) \(\chi_{3234}(1369,\cdot)\) \(\chi_{3234}(1411,\cdot)\) \(\chi_{3234}(1423,\cdot)\) \(\chi_{3234}(1621,\cdot)\) \(\chi_{3234}(1633,\cdot)\) \(\chi_{3234}(1675,\cdot)\) \(\chi_{3234}(1747,\cdot)\) \(\chi_{3234}(1873,\cdot)\) \(\chi_{3234}(1885,\cdot)\) \(\chi_{3234}(2011,\cdot)\) ...

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{8}{21}\right),e\left(\frac{4}{5}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{26}{105}\right)\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{76}{105}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{52}{105}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{83}{105}\right)\)\(e\left(\frac{4}{35}\right)\)
value at  e.g. 2

Related number fields

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