Properties

Label 571.h
Modulus $571$
Conductor $571$
Order $19$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(571, base_ring=CyclotomicField(38))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(31,571))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(571\)
Conductor: \(571\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(19\)
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: 19.19.41634173570364661205169708858211372543325791407961.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(31,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\)
\(\chi_{571}(55,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{571}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{571}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{571}(94,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{571}(99,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{571}(116,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{571}(131,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{571}(170,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{571}(214,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{571}(271,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{571}(306,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{571}(323,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{571}(350,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{571}(353,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{571}(390,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{571}(407,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{571}(563,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{14}{19}\right)\)