Properties

Label 916.p
Modulus $916$
Conductor $916$
Order $38$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(916, base_ring=CyclotomicField(38))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([19,28]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(27,916))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(916\)
Conductor: \(916\)
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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{19})\)
Fixed field: 38.0.2472960613492762938009352687218362626942035203162587025151809700624254848124906369677396881178624.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{916}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{916}(43,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{916}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{916}(271,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{916}(443,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{916}(447,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{6}{19}\right)\)
\(\chi_{916}(475,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{916}(511,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{916}(515,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{916}(519,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{916}(579,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{916}(619,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{916}(623,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{916}(683,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{916}(703,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{916}(731,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{916}(747,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{916}(791,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{13}{19}\right)\)