Properties

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

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[19]
 
pari: [g,chi] = znchar(Mod(19,4730))
 

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.dh
Orbit index = 86

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 ]
 

\(\chi_{4730}(19,\cdot)\) \(\chi_{4730}(29,\cdot)\) \(\chi_{4730}(149,\cdot)\) \(\chi_{4730}(249,\cdot)\) \(\chi_{4730}(349,\cdot)\) \(\chi_{4730}(459,\cdot)\) \(\chi_{4730}(519,\cdot)\) \(\chi_{4730}(579,\cdot)\) \(\chi_{4730}(589,\cdot)\) \(\chi_{4730}(679,\cdot)\) \(\chi_{4730}(1009,\cdot)\) \(\chi_{4730}(1019,\cdot)\) \(\chi_{4730}(1179,\cdot)\) \(\chi_{4730}(1359,\cdot)\) \(\chi_{4730}(1449,\cdot)\) \(\chi_{4730}(1619,\cdot)\) \(\chi_{4730}(1689,\cdot)\) \(\chi_{4730}(1789,\cdot)\) \(\chi_{4730}(1839,\cdot)\) \(\chi_{4730}(2119,\cdot)\) \(\chi_{4730}(2169,\cdot)\) \(\chi_{4730}(2219,\cdot)\) \(\chi_{4730}(2239,\cdot)\) \(\chi_{4730}(2499,\cdot)\) \(\chi_{4730}(2549,\cdot)\) \(\chi_{4730}(2609,\cdot)\) \(\chi_{4730}(2669,\cdot)\) \(\chi_{4730}(2829,\cdot)\) \(\chi_{4730}(2899,\cdot)\) \(\chi_{4730}(3099,\cdot)\) ...

Values on generators

\((947,431,1981)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{19}{42}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{37}{105}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{74}{105}\right)\)\(e\left(\frac{29}{105}\right)\)\(e\left(\frac{41}{105}\right)\)\(e\left(\frac{52}{105}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{2}{35}\right)\)\(e\left(\frac{68}{105}\right)\)
value at  e.g. 2

Related number fields

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