Properties

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

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[13]
 
pari: [g,chi] = znchar(Mod(13,4730))
 

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.dp
Orbit index = 94

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 ]
 

\(\chi_{4730}(13,\cdot)\) \(\chi_{4730}(17,\cdot)\) \(\chi_{4730}(57,\cdot)\) \(\chi_{4730}(83,\cdot)\) \(\chi_{4730}(117,\cdot)\) \(\chi_{4730}(167,\cdot)\) \(\chi_{4730}(283,\cdot)\) \(\chi_{4730}(447,\cdot)\) \(\chi_{4730}(453,\cdot)\) \(\chi_{4730}(497,\cdot)\) \(\chi_{4730}(513,\cdot)\) \(\chi_{4730}(547,\cdot)\) \(\chi_{4730}(633,\cdot)\) \(\chi_{4730}(783,\cdot)\) \(\chi_{4730}(787,\cdot)\) \(\chi_{4730}(827,\cdot)\) \(\chi_{4730}(877,\cdot)\) \(\chi_{4730}(943,\cdot)\) \(\chi_{4730}(963,\cdot)\) \(\chi_{4730}(1003,\cdot)\) \(\chi_{4730}(1047,\cdot)\) \(\chi_{4730}(1063,\cdot)\) \(\chi_{4730}(1113,\cdot)\) \(\chi_{4730}(1217,\cdot)\) \(\chi_{4730}(1227,\cdot)\) \(\chi_{4730}(1393,\cdot)\) \(\chi_{4730}(1443,\cdot)\) \(\chi_{4730}(1487,\cdot)\) \(\chi_{4730}(1493,\cdot)\) \(\chi_{4730}(1557,\cdot)\) ...

Values on generators

\((947,431,1981)\) → \((-i,e\left(\frac{1}{10}\right),e\left(\frac{16}{21}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{341}{420}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{131}{210}\right)\)\(e\left(\frac{307}{420}\right)\)\(e\left(\frac{253}{420}\right)\)\(e\left(\frac{29}{105}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{37}{84}\right)\)\(e\left(\frac{61}{140}\right)\)\(e\left(\frac{46}{105}\right)\)
value at  e.g. 2

Related number fields

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