Properties

Label 143.r
Modulus $143$
Conductor $143$
Order $20$
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(20))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,15]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(5,143))
 
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: \(20\)
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: \(\Q(\zeta_{20})\)
Fixed field: Number field defined by a degree 20 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{143}(5,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(47,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(60,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(70,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(86,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(125,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(135,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(-1\)