Properties

Conductor 539
Order 35
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.bp

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[169]
 
pari: [g,chi] = znchar(Mod(169,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 539
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 35
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.bp
Orbit index = 42

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 ]
 

\(\chi_{3234}(169,\cdot)\) \(\chi_{3234}(379,\cdot)\) \(\chi_{3234}(421,\cdot)\) \(\chi_{3234}(631,\cdot)\) \(\chi_{3234}(757,\cdot)\) \(\chi_{3234}(841,\cdot)\) \(\chi_{3234}(1093,\cdot)\) \(\chi_{3234}(1219,\cdot)\) \(\chi_{3234}(1303,\cdot)\) \(\chi_{3234}(1345,\cdot)\) \(\chi_{3234}(1555,\cdot)\) \(\chi_{3234}(1681,\cdot)\) \(\chi_{3234}(1807,\cdot)\) \(\chi_{3234}(2017,\cdot)\) \(\chi_{3234}(2143,\cdot)\) \(\chi_{3234}(2227,\cdot)\) \(\chi_{3234}(2269,\cdot)\) \(\chi_{3234}(2479,\cdot)\) \(\chi_{3234}(2605,\cdot)\) \(\chi_{3234}(2689,\cdot)\) \(\chi_{3234}(2731,\cdot)\) \(\chi_{3234}(3067,\cdot)\) \(\chi_{3234}(3151,\cdot)\) \(\chi_{3234}(3193,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{4}{7}\right),e\left(\frac{1}{5}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{2}{35}\right)\)\(e\left(\frac{3}{35}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{6}{35}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)