Properties

Conductor 675
Order 180
Real no
Primitive no
Minimal yes
Parity even
Orbit label 1350.bi

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[23]
 
pari: [g,chi] = znchar(Mod(23,1350))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 675
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 180
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.bi
Orbit index = 35

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 ]
 

\(\chi_{1350}(23,\cdot)\) \(\chi_{1350}(47,\cdot)\) \(\chi_{1350}(77,\cdot)\) \(\chi_{1350}(83,\cdot)\) \(\chi_{1350}(113,\cdot)\) \(\chi_{1350}(137,\cdot)\) \(\chi_{1350}(167,\cdot)\) \(\chi_{1350}(173,\cdot)\) \(\chi_{1350}(203,\cdot)\) \(\chi_{1350}(227,\cdot)\) \(\chi_{1350}(263,\cdot)\) \(\chi_{1350}(317,\cdot)\) \(\chi_{1350}(347,\cdot)\) \(\chi_{1350}(353,\cdot)\) \(\chi_{1350}(383,\cdot)\) \(\chi_{1350}(437,\cdot)\) \(\chi_{1350}(473,\cdot)\) \(\chi_{1350}(497,\cdot)\) \(\chi_{1350}(527,\cdot)\) \(\chi_{1350}(533,\cdot)\) \(\chi_{1350}(563,\cdot)\) \(\chi_{1350}(587,\cdot)\) \(\chi_{1350}(617,\cdot)\) \(\chi_{1350}(623,\cdot)\) \(\chi_{1350}(653,\cdot)\) \(\chi_{1350}(677,\cdot)\) \(\chi_{1350}(713,\cdot)\) \(\chi_{1350}(767,\cdot)\) \(\chi_{1350}(797,\cdot)\) \(\chi_{1350}(803,\cdot)\) ...

Values on generators

\((1001,1027)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{11}{20}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{67}{90}\right)\)\(e\left(\frac{61}{180}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{139}{180}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{53}{90}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{180})\)