Properties

Conductor 675
Order 90
Real no
Primitive no
Minimal yes
Parity even
Orbit label 1350.bf

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[79]
 
pari: [g,chi] = znchar(Mod(79,1350))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 675
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1350.bf
Orbit index = 32

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 ]
 

\(\chi_{1350}(79,\cdot)\) \(\chi_{1350}(139,\cdot)\) \(\chi_{1350}(169,\cdot)\) \(\chi_{1350}(229,\cdot)\) \(\chi_{1350}(259,\cdot)\) \(\chi_{1350}(319,\cdot)\) \(\chi_{1350}(409,\cdot)\) \(\chi_{1350}(439,\cdot)\) \(\chi_{1350}(529,\cdot)\) \(\chi_{1350}(589,\cdot)\) \(\chi_{1350}(619,\cdot)\) \(\chi_{1350}(679,\cdot)\) \(\chi_{1350}(709,\cdot)\) \(\chi_{1350}(769,\cdot)\) \(\chi_{1350}(859,\cdot)\) \(\chi_{1350}(889,\cdot)\) \(\chi_{1350}(979,\cdot)\) \(\chi_{1350}(1039,\cdot)\) \(\chi_{1350}(1069,\cdot)\) \(\chi_{1350}(1129,\cdot)\) \(\chi_{1350}(1159,\cdot)\) \(\chi_{1350}(1219,\cdot)\) \(\chi_{1350}(1309,\cdot)\) \(\chi_{1350}(1339,\cdot)\)

Values on generators

\((1001,1027)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{10}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{37}{45}\right)\)\(e\left(\frac{31}{90}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{19}{90}\right)\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{41}{45}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{38}{45}\right)\)
value at  e.g. 2

Related number fields

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