Properties

Conductor 539
Order 70
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.ca

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[13]
 
pari: [g,chi] = znchar(Mod(13,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 539
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
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.ca
Orbit index = 53

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 ]
 

\(\chi_{3234}(13,\cdot)\) \(\chi_{3234}(139,\cdot)\) \(\chi_{3234}(349,\cdot)\) \(\chi_{3234}(475,\cdot)\) \(\chi_{3234}(601,\cdot)\) \(\chi_{3234}(811,\cdot)\) \(\chi_{3234}(853,\cdot)\) \(\chi_{3234}(937,\cdot)\) \(\chi_{3234}(1063,\cdot)\) \(\chi_{3234}(1315,\cdot)\) \(\chi_{3234}(1399,\cdot)\) \(\chi_{3234}(1525,\cdot)\) \(\chi_{3234}(1735,\cdot)\) \(\chi_{3234}(1777,\cdot)\) \(\chi_{3234}(1987,\cdot)\) \(\chi_{3234}(2197,\cdot)\) \(\chi_{3234}(2239,\cdot)\) \(\chi_{3234}(2323,\cdot)\) \(\chi_{3234}(2659,\cdot)\) \(\chi_{3234}(2701,\cdot)\) \(\chi_{3234}(2785,\cdot)\) \(\chi_{3234}(2911,\cdot)\) \(\chi_{3234}(3121,\cdot)\) \(\chi_{3234}(3163,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{13}{70}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{3}{35}\right)\)
value at  e.g. 2

Related number fields

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