Properties

Conductor 675
Order 45
Real no
Primitive no
Minimal yes
Parity even
Orbit label 1350.bc

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(1350)
 
sage: chi = H[31]
 
pari: [g,chi] = znchar(Mod(31,1350))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 675
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 45
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 = 1350.bc
Orbit index = 29

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 ]
 

\(\chi_{1350}(31,\cdot)\) \(\chi_{1350}(61,\cdot)\) \(\chi_{1350}(121,\cdot)\) \(\chi_{1350}(211,\cdot)\) \(\chi_{1350}(241,\cdot)\) \(\chi_{1350}(331,\cdot)\) \(\chi_{1350}(391,\cdot)\) \(\chi_{1350}(421,\cdot)\) \(\chi_{1350}(481,\cdot)\) \(\chi_{1350}(511,\cdot)\) \(\chi_{1350}(571,\cdot)\) \(\chi_{1350}(661,\cdot)\) \(\chi_{1350}(691,\cdot)\) \(\chi_{1350}(781,\cdot)\) \(\chi_{1350}(841,\cdot)\) \(\chi_{1350}(871,\cdot)\) \(\chi_{1350}(931,\cdot)\) \(\chi_{1350}(961,\cdot)\) \(\chi_{1350}(1021,\cdot)\) \(\chi_{1350}(1111,\cdot)\) \(\chi_{1350}(1141,\cdot)\) \(\chi_{1350}(1231,\cdot)\) \(\chi_{1350}(1291,\cdot)\) \(\chi_{1350}(1321,\cdot)\)

Values on generators

\((1001,1027)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{2}{5}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{38}{45}\right)\)\(e\left(\frac{22}{45}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{41}{45}\right)\)\(e\left(\frac{19}{45}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{22}{45}\right)\)
value at  e.g. 2

Related number fields

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