Properties

Label 517.l
Modulus $517$
Conductor $517$
Order $46$
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(517, base_ring=CyclotomicField(46))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([23,19]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(10,517))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(517\)
Conductor: \(517\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(46\)
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: \(\Q(\zeta_{23})\)
Fixed field: 46.46.1571937830040451992228674568491756687115540075866136861286122171472474917522743511699927590412842317.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{517}(10,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{517}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{517}(76,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{517}(87,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{517}(109,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{517}(120,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{517}(164,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{517}(186,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{517}(208,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{517}(219,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{517}(274,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{517}(340,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{517}(351,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{517}(362,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{517}(373,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{517}(395,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{517}(406,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{517}(417,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{517}(428,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{517}(461,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{517}(483,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{517}(505,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{4}{23}\right)\)