Properties

Conductor 547
Order 91
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.bl

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(6017)
 
sage: chi = H[100]
 
pari: [g,chi] = znchar(Mod(100,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 547
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 91
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 = 6017.bl
Orbit index = 38

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 ]
 

\(\chi_{6017}(100,\cdot)\) \(\chi_{6017}(309,\cdot)\) \(\chi_{6017}(661,\cdot)\) \(\chi_{6017}(771,\cdot)\) \(\chi_{6017}(815,\cdot)\) \(\chi_{6017}(837,\cdot)\) \(\chi_{6017}(969,\cdot)\) \(\chi_{6017}(991,\cdot)\) \(\chi_{6017}(1123,\cdot)\) \(\chi_{6017}(1178,\cdot)\) \(\chi_{6017}(1255,\cdot)\) \(\chi_{6017}(1299,\cdot)\) \(\chi_{6017}(1310,\cdot)\) \(\chi_{6017}(1376,\cdot)\) \(\chi_{6017}(1409,\cdot)\) \(\chi_{6017}(1508,\cdot)\) \(\chi_{6017}(1552,\cdot)\) \(\chi_{6017}(1651,\cdot)\) \(\chi_{6017}(1772,\cdot)\) \(\chi_{6017}(1904,\cdot)\) \(\chi_{6017}(2157,\cdot)\) \(\chi_{6017}(2212,\cdot)\) \(\chi_{6017}(2223,\cdot)\) \(\chi_{6017}(2278,\cdot)\) \(\chi_{6017}(2355,\cdot)\) \(\chi_{6017}(2465,\cdot)\) \(\chi_{6017}(2509,\cdot)\) \(\chi_{6017}(2597,\cdot)\) \(\chi_{6017}(2630,\cdot)\) \(\chi_{6017}(2641,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{60}{91}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{60}{91}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{29}{91}\right)\)\(e\left(\frac{2}{91}\right)\)\(e\left(\frac{47}{91}\right)\)\(e\left(\frac{83}{91}\right)\)\(e\left(\frac{89}{91}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{62}{91}\right)\)\(e\left(\frac{16}{91}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{91})\)