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Properties

Label 1083.m
Modulus $1083$
Conductor $361$
Order $19$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1083, base_ring=CyclotomicField(38)) M = H._module chi = DirichletCharacter(H, M([0,2])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(58,1083)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1083\)
Conductor: \(361\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(19\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 361.g
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{19})\)
Fixed field: 19.19.10842505080063916320800450434338728415281531281.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{1083}(58,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{1083}(115,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{1083}(172,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{1083}(229,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{1083}(286,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{1083}(343,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{1083}(400,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{1083}(457,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{1083}(514,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{1083}(571,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{1083}(628,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{6}{19}\right)\)
\(\chi_{1083}(685,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{1083}(742,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{1083}(799,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{1083}(856,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{1083}(913,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{1083}(970,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{1083}(1027,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{15}{19}\right)\)