Properties

Label 287.x
Modulus $287$
Conductor $287$
Order $30$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(287, base_ring=CyclotomicField(30))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([5,21]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(31,287))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(287\)
Conductor: \(287\)
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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: 30.0.47056013503315267757707869738647378732273238450224554604301383567.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{287}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{287}(45,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{287}(66,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{287}(187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{287}(236,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{287}(250,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{287}(269,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{287}(271,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{15}\right)\)