Properties

Label 1805.q
Modulus $1805$
Conductor $361$
Order $19$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1805, base_ring=CyclotomicField(38))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,16]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(96,1805))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1805\)
Conductor: \(361\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(19\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 361.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: 19.19.10842505080063916320800450434338728415281531281.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{1805}(96,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{1805}(191,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{1805}(286,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{1805}(381,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{1805}(476,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{1805}(571,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{1805}(666,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{1805}(761,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{1805}(856,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{1805}(951,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{1805}(1046,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{1805}(1141,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{6}{19}\right)\)
\(\chi_{1805}(1236,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{1805}(1331,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{1805}(1426,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{1805}(1521,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{1805}(1616,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{1805}(1711,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{9}{19}\right)\)