Properties

Conductor 1617
Order 70
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.by

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[29]
 
pari: [g,chi] = znchar(Mod(29,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1617
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.by
Orbit index = 51

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 ]
 

\(\chi_{3234}(29,\cdot)\) \(\chi_{3234}(239,\cdot)\) \(\chi_{3234}(281,\cdot)\) \(\chi_{3234}(365,\cdot)\) \(\chi_{3234}(701,\cdot)\) \(\chi_{3234}(743,\cdot)\) \(\chi_{3234}(827,\cdot)\) \(\chi_{3234}(953,\cdot)\) \(\chi_{3234}(1163,\cdot)\) \(\chi_{3234}(1205,\cdot)\) \(\chi_{3234}(1289,\cdot)\) \(\chi_{3234}(1415,\cdot)\) \(\chi_{3234}(1625,\cdot)\) \(\chi_{3234}(1751,\cdot)\) \(\chi_{3234}(1877,\cdot)\) \(\chi_{3234}(2087,\cdot)\) \(\chi_{3234}(2129,\cdot)\) \(\chi_{3234}(2213,\cdot)\) \(\chi_{3234}(2339,\cdot)\) \(\chi_{3234}(2591,\cdot)\) \(\chi_{3234}(2675,\cdot)\) \(\chi_{3234}(2801,\cdot)\) \(\chi_{3234}(3011,\cdot)\) \(\chi_{3234}(3053,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((-1,e\left(\frac{3}{7}\right),e\left(\frac{7}{10}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{51}{70}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{4}{35}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{4}{35}\right)\)\(e\left(\frac{1}{35}\right)\)
value at  e.g. 2

Related number fields

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