Properties

Label 1375.br
Modulus $1375$
Conductor $1375$
Order $25$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1375, base_ring=CyclotomicField(50))
 
M = H._module
 
chi = DirichletCharacter(H, M([2,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(16,1375))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1375\)
Conductor: \(1375\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(25\)
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: \(\Q(\zeta_{25})\)
Fixed field: 25.25.227936564389216769066972959924266550757465665810741484165191650390625.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1375}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{1375}(86,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{1375}(246,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{1375}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{1375}(291,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{1375}(361,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{1375}(521,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{1375}(531,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{1375}(566,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{1375}(636,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{1375}(796,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{1375}(806,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{1375}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{1375}(911,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{1375}(1071,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{1375}(1081,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{1375}(1116,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{1375}(1186,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{1375}(1346,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{1375}(1356,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{22}{25}\right)\)