Properties

Label 1287.dw
Modulus $1287$
Conductor $1287$
Order $30$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1287, base_ring=CyclotomicField(30))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([10,6,5]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(4,1287))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1287\)
Conductor: \(1287\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{1287}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1287}(322,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1287}(355,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1287}(790,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1287}(823,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1287}(907,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1287}(940,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1287}(1258,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\)