Properties

Label 916.m
Modulus $916$
Conductor $229$
Order $19$
Real no
Primitive no
Minimal yes
Parity even

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([0,10]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(17,916))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(916\)
Conductor: \(229\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(19\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 229.g
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: 19.19.2999429662895796650415561622892044448017561.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{916}(17,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{916}(53,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{916}(57,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{916}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{916}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{916}(161,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{916}(165,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{916}(225,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{916}(245,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{916}(273,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{916}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{916}(333,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{916}(485,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{916}(501,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{916}(661,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{916}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{916}(901,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{916}(905,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\)