Properties

Conductor 2365
Order 210
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.dl

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[9]
 
pari: [g,chi] = znchar(Mod(9,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
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.dl
Orbit index = 90

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 ]
 

\(\chi_{4730}(9,\cdot)\) \(\chi_{4730}(169,\cdot)\) \(\chi_{4730}(229,\cdot)\) \(\chi_{4730}(289,\cdot)\) \(\chi_{4730}(339,\cdot)\) \(\chi_{4730}(599,\cdot)\) \(\chi_{4730}(619,\cdot)\) \(\chi_{4730}(669,\cdot)\) \(\chi_{4730}(719,\cdot)\) \(\chi_{4730}(999,\cdot)\) \(\chi_{4730}(1049,\cdot)\) \(\chi_{4730}(1149,\cdot)\) \(\chi_{4730}(1219,\cdot)\) \(\chi_{4730}(1389,\cdot)\) \(\chi_{4730}(1479,\cdot)\) \(\chi_{4730}(1659,\cdot)\) \(\chi_{4730}(1819,\cdot)\) \(\chi_{4730}(1829,\cdot)\) \(\chi_{4730}(2159,\cdot)\) \(\chi_{4730}(2249,\cdot)\) \(\chi_{4730}(2259,\cdot)\) \(\chi_{4730}(2319,\cdot)\) \(\chi_{4730}(2379,\cdot)\) \(\chi_{4730}(2489,\cdot)\) \(\chi_{4730}(2589,\cdot)\) \(\chi_{4730}(2689,\cdot)\) \(\chi_{4730}(2809,\cdot)\) \(\chi_{4730}(2819,\cdot)\) \(\chi_{4730}(2869,\cdot)\) \(\chi_{4730}(2919,\cdot)\) ...

Values on generators

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

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{73}{210}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{73}{105}\right)\)\(e\left(\frac{131}{210}\right)\)\(e\left(\frac{149}{210}\right)\)\(e\left(\frac{74}{105}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{11}{42}\right)\)\(e\left(\frac{3}{70}\right)\)\(e\left(\frac{16}{105}\right)\)
value at  e.g. 2

Related number fields

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