Properties

Conductor 1007
Order 468
Real No
Primitive No
Parity Odd
Orbit Label 6042.cr

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6042)
 
sage: chi = H[85]
 
pari: [g,chi] = znchar(Mod(85,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 468
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 6042.cr
Orbit index = 70

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 ]
 

\(\chi_{6042}(55,\cdot)\) \(\chi_{6042}(61,\cdot)\) \(\chi_{6042}(73,\cdot)\) \(\chi_{6042}(85,\cdot)\) \(\chi_{6042}(139,\cdot)\) \(\chi_{6042}(157,\cdot)\) \(\chi_{6042}(253,\cdot)\) \(\chi_{6042}(283,\cdot)\) \(\chi_{6042}(313,\cdot)\) \(\chi_{6042}(385,\cdot)\) \(\chi_{6042}(397,\cdot)\) \(\chi_{6042}(403,\cdot)\) \(\chi_{6042}(427,\cdot)\) \(\chi_{6042}(499,\cdot)\) \(\chi_{6042}(511,\cdot)\) \(\chi_{6042}(595,\cdot)\) \(\chi_{6042}(631,\cdot)\) \(\chi_{6042}(655,\cdot)\) \(\chi_{6042}(709,\cdot)\) \(\chi_{6042}(739,\cdot)\) \(\chi_{6042}(745,\cdot)\) \(\chi_{6042}(769,\cdot)\) \(\chi_{6042}(853,\cdot)\) \(\chi_{6042}(883,\cdot)\) \(\chi_{6042}(973,\cdot)\) \(\chi_{6042}(985,\cdot)\) \(\chi_{6042}(1081,\cdot)\) \(\chi_{6042}(1087,\cdot)\) \(\chi_{6042}(1099,\cdot)\) \(\chi_{6042}(1111,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(85,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{4}{9}\right),e\left(\frac{5}{52}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{295}{468}\right)\)\(e\left(\frac{1}{78}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{62}{117}\right)\)\(e\left(\frac{95}{234}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{61}{234}\right)\)\(e\left(\frac{229}{234}\right)\)\(e\left(\frac{131}{156}\right)\)\(e\left(\frac{301}{468}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{468})\)