Properties

Label 5185.jj
Modulus $5185$
Conductor $1037$
Order $120$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(5185, base_ring=CyclotomicField(120))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,15,82]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(26,5185))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5185\)
Conductor: \(1037\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1037.cm
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: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{5185}(26,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(246,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(331,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(376,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(1141,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1226,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1386,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(1396,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1471,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1481,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(1596,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(1641,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1691,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(1726,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1776,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(1946,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(2031,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(2361,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(2446,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(2491,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(2616,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(2701,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(2796,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(2841,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(2926,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(3691,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(4061,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(4146,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(4361,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(4666,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(4911,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{5}{6}\right)\)