Properties

Conductor 473
Order 105
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.dc

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(4730)
 
sage: chi = H[31]
 
pari: [g,chi] = znchar(Mod(31,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 105
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 = 4730.dc
Orbit index = 81

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 ]
 

\(\chi_{4730}(31,\cdot)\) \(\chi_{4730}(81,\cdot)\) \(\chi_{4730}(181,\cdot)\) \(\chi_{4730}(311,\cdot)\) \(\chi_{4730}(361,\cdot)\) \(\chi_{4730}(401,\cdot)\) \(\chi_{4730}(411,\cdot)\) \(\chi_{4730}(511,\cdot)\) \(\chi_{4730}(531,\cdot)\) \(\chi_{4730}(741,\cdot)\) \(\chi_{4730}(841,\cdot)\) \(\chi_{4730}(961,\cdot)\) \(\chi_{4730}(971,\cdot)\) \(\chi_{4730}(1131,\cdot)\) \(\chi_{4730}(1171,\cdot)\) \(\chi_{4730}(1391,\cdot)\) \(\chi_{4730}(1401,\cdot)\) \(\chi_{4730}(1571,\cdot)\) \(\chi_{4730}(1631,\cdot)\) \(\chi_{4730}(1831,\cdot)\) \(\chi_{4730}(1901,\cdot)\) \(\chi_{4730}(2061,\cdot)\) \(\chi_{4730}(2121,\cdot)\) \(\chi_{4730}(2181,\cdot)\) \(\chi_{4730}(2231,\cdot)\) \(\chi_{4730}(2491,\cdot)\) \(\chi_{4730}(2511,\cdot)\) \(\chi_{4730}(2561,\cdot)\) \(\chi_{4730}(2611,\cdot)\) \(\chi_{4730}(2891,\cdot)\) ...

Values on generators

\((947,431,1981)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{17}{21}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{64}{105}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{23}{105}\right)\)\(e\left(\frac{53}{105}\right)\)\(e\left(\frac{17}{105}\right)\)\(e\left(\frac{19}{105}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{41}{105}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)