Properties

Modulus 4725
Conductor 4725
Order 90
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4725.gm

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4725)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([5,54,45]))
 
pari: [g,chi] = znchar(Mod(3296,4725))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4725
Conductor = 4725
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 90
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4725.gm
Orbit index = 169

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4725}(41,\cdot)\) \(\chi_{4725}(146,\cdot)\) \(\chi_{4725}(356,\cdot)\) \(\chi_{4725}(461,\cdot)\) \(\chi_{4725}(671,\cdot)\) \(\chi_{4725}(986,\cdot)\) \(\chi_{4725}(1091,\cdot)\) \(\chi_{4725}(1406,\cdot)\) \(\chi_{4725}(1616,\cdot)\) \(\chi_{4725}(1721,\cdot)\) \(\chi_{4725}(1931,\cdot)\) \(\chi_{4725}(2036,\cdot)\) \(\chi_{4725}(2246,\cdot)\) \(\chi_{4725}(2561,\cdot)\) \(\chi_{4725}(2666,\cdot)\) \(\chi_{4725}(2981,\cdot)\) \(\chi_{4725}(3191,\cdot)\) \(\chi_{4725}(3296,\cdot)\) \(\chi_{4725}(3506,\cdot)\) \(\chi_{4725}(3611,\cdot)\) \(\chi_{4725}(3821,\cdot)\) \(\chi_{4725}(4136,\cdot)\) \(\chi_{4725}(4241,\cdot)\) \(\chi_{4725}(4556,\cdot)\)

Values on generators

\((4376,1702,2026)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{5}\right),-1)\)

Values

-1124811131617192223
\(1\)\(1\)\(e\left(\frac{59}{90}\right)\)\(e\left(\frac{14}{45}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{29}{90}\right)\)\(e\left(\frac{31}{90}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{44}{45}\right)\)\(e\left(\frac{19}{90}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{45})\)