Properties

Conductor 473
Order 210
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.dn

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[61]
 
pari: [g,chi] = znchar(Mod(61,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
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.dn
Orbit index = 92

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 ]
 

\(\chi_{4730}(61,\cdot)\) \(\chi_{4730}(261,\cdot)\) \(\chi_{4730}(321,\cdot)\) \(\chi_{4730}(491,\cdot)\) \(\chi_{4730}(501,\cdot)\) \(\chi_{4730}(721,\cdot)\) \(\chi_{4730}(761,\cdot)\) \(\chi_{4730}(921,\cdot)\) \(\chi_{4730}(931,\cdot)\) \(\chi_{4730}(1051,\cdot)\) \(\chi_{4730}(1151,\cdot)\) \(\chi_{4730}(1361,\cdot)\) \(\chi_{4730}(1381,\cdot)\) \(\chi_{4730}(1481,\cdot)\) \(\chi_{4730}(1491,\cdot)\) \(\chi_{4730}(1531,\cdot)\) \(\chi_{4730}(1581,\cdot)\) \(\chi_{4730}(1711,\cdot)\) \(\chi_{4730}(1811,\cdot)\) \(\chi_{4730}(1861,\cdot)\) \(\chi_{4730}(1911,\cdot)\) \(\chi_{4730}(1921,\cdot)\) \(\chi_{4730}(2041,\cdot)\) \(\chi_{4730}(2141,\cdot)\) \(\chi_{4730}(2241,\cdot)\) \(\chi_{4730}(2351,\cdot)\) \(\chi_{4730}(2411,\cdot)\) \(\chi_{4730}(2471,\cdot)\) \(\chi_{4730}(2481,\cdot)\) \(\chi_{4730}(2571,\cdot)\) ...

Values on generators

\((947,431,1981)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{29}{42}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{187}{210}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{82}{105}\right)\)\(e\left(\frac{209}{210}\right)\)\(e\left(\frac{71}{210}\right)\)\(e\left(\frac{86}{105}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{47}{70}\right)\)\(e\left(\frac{64}{105}\right)\)
value at  e.g. 2

Related number fields

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