Properties

Label 675.y
Modulus $675$
Conductor $225$
Order $30$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(675, base_ring=CyclotomicField(30))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([20,27]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(19,675))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(675\)
Conductor: \(225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 225.u
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: 30.30.5399088047333990303844331037907977588474750518798828125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{675}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{675}(154,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{675}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{675}(334,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{675}(469,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(559,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{675}(604,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)