Properties

Label 764.l
Modulus $764$
Conductor $764$
Order $38$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(764, base_ring=CyclotomicField(38))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([19,17]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(11,764))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(764\)
Conductor: \(764\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(38\)
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: \(\Q(\zeta_{19})\)
Fixed field: 38.38.687661045808093482376579225097085116287670624782479569073265850359469722789446885178751177457664.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{764}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{38}\right)\)
\(\chi_{764}(31,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{38}\right)\)
\(\chi_{764}(55,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{35}{38}\right)\)
\(\chi_{764}(139,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{23}{38}\right)\)
\(\chi_{764}(155,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{33}{38}\right)\)
\(\chi_{764}(159,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{31}{38}\right)\)
\(\chi_{764}(275,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{38}\right)\)
\(\chi_{764}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{25}{38}\right)\)
\(\chi_{764}(423,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{38}\right)\)
\(\chi_{764}(543,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{27}{38}\right)\)
\(\chi_{764}(567,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{7}{38}\right)\)
\(\chi_{764}(587,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{29}{38}\right)\)
\(\chi_{764}(611,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{37}{38}\right)\)
\(\chi_{764}(639,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{38}\right)\)
\(\chi_{764}(643,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{38}\right)\)
\(\chi_{764}(695,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{38}\right)\)
\(\chi_{764}(739,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{21}{38}\right)\)
\(\chi_{764}(759,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{38}\right)\)