Properties

Label 517.j
Modulus $517$
Conductor $47$
Order $46$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(517, base_ring=CyclotomicField(46))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,5]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(23,517))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(517\)
Conductor: \(47\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(46\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 47.d
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: \(\Q(\zeta_{23})\)
Fixed field: \(\Q(\zeta_{47})\)

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{517}(23,\cdot)\) \(-1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{517}(45,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{517}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{517}(78,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{517}(133,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{517}(199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{517}(210,\cdot)\) \(-1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{517}(221,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{517}(232,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{517}(254,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{517}(265,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{517}(276,\cdot)\) \(-1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{517}(287,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{517}(320,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{517}(342,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{517}(364,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{517}(386,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{517}(419,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{517}(452,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{517}(463,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{517}(485,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{517}(496,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{7}{23}\right)\)