Properties

Label 143.v
Modulus $143$
Conductor $143$
Order $30$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([27,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(17,143))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(143\)
Conductor: \(143\)
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: 30.0.92509494307745903779193517092075417558886189689936206103.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{143}(17,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(30,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(62,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{143}(95,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{143}(127,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{143}(134,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(140,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)