Properties

Conductor 1007
Order 156
Real No
Primitive No
Parity Even
Orbit Label 6042.ch

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[31]
 
pari: [g,chi] = znchar(Mod(31,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 156
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 = Even
Orbit label = 6042.ch
Orbit index = 60

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 ]
 

\(\chi_{6042}(31,\cdot)\) \(\chi_{6042}(103,\cdot)\) \(\chi_{6042}(145,\cdot)\) \(\chi_{6042}(217,\cdot)\) \(\chi_{6042}(373,\cdot)\) \(\chi_{6042}(445,\cdot)\) \(\chi_{6042}(601,\cdot)\) \(\chi_{6042}(715,\cdot)\) \(\chi_{6042}(787,\cdot)\) \(\chi_{6042}(829,\cdot)\) \(\chi_{6042}(1015,\cdot)\) \(\chi_{6042}(1057,\cdot)\) \(\chi_{6042}(1171,\cdot)\) \(\chi_{6042}(1357,\cdot)\) \(\chi_{6042}(1399,\cdot)\) \(\chi_{6042}(1585,\cdot)\) \(\chi_{6042}(1699,\cdot)\) \(\chi_{6042}(1741,\cdot)\) \(\chi_{6042}(1927,\cdot)\) \(\chi_{6042}(1969,\cdot)\) \(\chi_{6042}(2041,\cdot)\) \(\chi_{6042}(2155,\cdot)\) \(\chi_{6042}(2311,\cdot)\) \(\chi_{6042}(2383,\cdot)\) \(\chi_{6042}(2539,\cdot)\) \(\chi_{6042}(2611,\cdot)\) \(\chi_{6042}(2653,\cdot)\) \(\chi_{6042}(2725,\cdot)\) \(\chi_{6042}(2881,\cdot)\) \(\chi_{6042}(2995,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(31,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{33}{52}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{25}{156}\right)\)\(e\left(\frac{23}{26}\right)\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{53}{78}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{23}{52}\right)\)\(e\left(\frac{7}{156}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{156})\)