Properties

Conductor 2365
Order 420
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.do

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[3]
 
pari: [g,chi] = znchar(Mod(3,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 420
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.do
Orbit index = 93

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 ]
 

\(\chi_{4730}(3,\cdot)\) \(\chi_{4730}(147,\cdot)\) \(\chi_{4730}(157,\cdot)\) \(\chi_{4730}(163,\cdot)\) \(\chi_{4730}(313,\cdot)\) \(\chi_{4730}(377,\cdot)\) \(\chi_{4730}(433,\cdot)\) \(\chi_{4730}(493,\cdot)\) \(\chi_{4730}(577,\cdot)\) \(\chi_{4730}(587,\cdot)\) \(\chi_{4730}(663,\cdot)\) \(\chi_{4730}(707,\cdot)\) \(\chi_{4730}(757,\cdot)\) \(\chi_{4730}(807,\cdot)\) \(\chi_{4730}(863,\cdot)\) \(\chi_{4730}(933,\cdot)\) \(\chi_{4730}(1017,\cdot)\) \(\chi_{4730}(1037,\cdot)\) \(\chi_{4730}(1087,\cdot)\) \(\chi_{4730}(1093,\cdot)\) \(\chi_{4730}(1103,\cdot)\) \(\chi_{4730}(1137,\cdot)\) \(\chi_{4730}(1147,\cdot)\) \(\chi_{4730}(1237,\cdot)\) \(\chi_{4730}(1323,\cdot)\) \(\chi_{4730}(1367,\cdot)\) \(\chi_{4730}(1467,\cdot)\) \(\chi_{4730}(1523,\cdot)\) \(\chi_{4730}(1533,\cdot)\) \(\chi_{4730}(1567,\cdot)\) ...

Values on generators

\((947,431,1981)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{1}{42}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{283}{420}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{73}{210}\right)\)\(e\left(\frac{341}{420}\right)\)\(e\left(\frac{359}{420}\right)\)\(e\left(\frac{37}{105}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{53}{84}\right)\)\(e\left(\frac{3}{140}\right)\)\(e\left(\frac{8}{105}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{420})\)