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Properties

Label 967.j
Modulus 967967
Conductor 967967
Order 4646
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(967, base_ring=CyclotomicField(46))
 
M = H._module
 
chi = DirichletCharacter(H, M([21]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(14,967))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 967967
Conductor: 967967
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4646
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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(ζ23)\Q(\zeta_{23})
Fixed field: Number field defined by a degree 46 polynomial

Characters in Galois orbit

Character −1-1 11 22 33 44 55 66 77 88 99 1010 1111
χ967(14,⋅)\chi_{967}(14,\cdot) −1-1 11 e(1723)e\left(\frac{17}{23}\right) e(946)e\left(\frac{9}{46}\right) e(1123)e\left(\frac{11}{23}\right) e(2146)e\left(\frac{21}{46}\right) e(4346)e\left(\frac{43}{46}\right) e(2746)e\left(\frac{27}{46}\right) e(523)e\left(\frac{5}{23}\right) e(923)e\left(\frac{9}{23}\right) e(946)e\left(\frac{9}{46}\right) e(923)e\left(\frac{9}{23}\right)
χ967(41,⋅)\chi_{967}(41,\cdot) −1-1 11 e(1523)e\left(\frac{15}{23}\right) e(3546)e\left(\frac{35}{46}\right) e(723)e\left(\frac{7}{23}\right) e(546)e\left(\frac{5}{46}\right) e(1946)e\left(\frac{19}{46}\right) e(1346)e\left(\frac{13}{46}\right) e(2223)e\left(\frac{22}{23}\right) e(1223)e\left(\frac{12}{23}\right) e(3546)e\left(\frac{35}{46}\right) e(1223)e\left(\frac{12}{23}\right)
χ967(51,⋅)\chi_{967}(51,\cdot) −1-1 11 e(1323)e\left(\frac{13}{23}\right) e(1546)e\left(\frac{15}{46}\right) e(323)e\left(\frac{3}{23}\right) e(3546)e\left(\frac{35}{46}\right) e(4146)e\left(\frac{41}{46}\right) e(4546)e\left(\frac{45}{46}\right) e(1623)e\left(\frac{16}{23}\right) e(1523)e\left(\frac{15}{23}\right) e(1546)e\left(\frac{15}{46}\right) e(1523)e\left(\frac{15}{23}\right)
χ967(74,⋅)\chi_{967}(74,\cdot) −1-1 11 e(1223)e\left(\frac{12}{23}\right) e(546)e\left(\frac{5}{46}\right) e(123)e\left(\frac{1}{23}\right) e(2746)e\left(\frac{27}{46}\right) e(2946)e\left(\frac{29}{46}\right) e(1546)e\left(\frac{15}{46}\right) e(1323)e\left(\frac{13}{23}\right) e(523)e\left(\frac{5}{23}\right) e(546)e\left(\frac{5}{46}\right) e(523)e\left(\frac{5}{23}\right)
χ967(94,⋅)\chi_{967}(94,\cdot) −1-1 11 e(223)e\left(\frac{2}{23}\right) e(4346)e\left(\frac{43}{46}\right) e(423)e\left(\frac{4}{23}\right) e(3946)e\left(\frac{39}{46}\right) e(146)e\left(\frac{1}{46}\right) e(3746)e\left(\frac{37}{46}\right) e(623)e\left(\frac{6}{23}\right) e(2023)e\left(\frac{20}{23}\right) e(4346)e\left(\frac{43}{46}\right) e(2023)e\left(\frac{20}{23}\right)
χ967(172,⋅)\chi_{967}(172,\cdot) −1-1 11 e(1623)e\left(\frac{16}{23}\right) e(4546)e\left(\frac{45}{46}\right) e(923)e\left(\frac{9}{23}\right) e(1346)e\left(\frac{13}{46}\right) e(3146)e\left(\frac{31}{46}\right) e(4346)e\left(\frac{43}{46}\right) e(223)e\left(\frac{2}{23}\right) e(2223)e\left(\frac{22}{23}\right) e(4546)e\left(\frac{45}{46}\right) e(2223)e\left(\frac{22}{23}\right)
χ967(253,⋅)\chi_{967}(253,\cdot) −1-1 11 e(723)e\left(\frac{7}{23}\right) e(146)e\left(\frac{1}{46}\right) e(1423)e\left(\frac{14}{23}\right) e(3346)e\left(\frac{33}{46}\right) e(1546)e\left(\frac{15}{46}\right) e(346)e\left(\frac{3}{46}\right) e(2123)e\left(\frac{21}{23}\right) e(123)e\left(\frac{1}{23}\right) e(146)e\left(\frac{1}{46}\right) e(123)e\left(\frac{1}{23}\right)
χ967(264,⋅)\chi_{967}(264,\cdot) −1-1 11 e(2223)e\left(\frac{22}{23}\right) e(1346)e\left(\frac{13}{46}\right) e(2123)e\left(\frac{21}{23}\right) e(1546)e\left(\frac{15}{46}\right) e(1146)e\left(\frac{11}{46}\right) e(3946)e\left(\frac{39}{46}\right) e(2023)e\left(\frac{20}{23}\right) e(1323)e\left(\frac{13}{23}\right) e(1346)e\left(\frac{13}{46}\right) e(1323)e\left(\frac{13}{23}\right)
χ967(271,⋅)\chi_{967}(271,\cdot) −1-1 11 e(1823)e\left(\frac{18}{23}\right) e(1946)e\left(\frac{19}{46}\right) e(1323)e\left(\frac{13}{23}\right) e(2946)e\left(\frac{29}{46}\right) e(946)e\left(\frac{9}{46}\right) e(1146)e\left(\frac{11}{46}\right) e(823)e\left(\frac{8}{23}\right) e(1923)e\left(\frac{19}{23}\right) e(1946)e\left(\frac{19}{46}\right) e(1923)e\left(\frac{19}{23}\right)
χ967(300,⋅)\chi_{967}(300,\cdot) −1-1 11 e(323)e\left(\frac{3}{23}\right) e(746)e\left(\frac{7}{46}\right) e(623)e\left(\frac{6}{23}\right) e(146)e\left(\frac{1}{46}\right) e(1346)e\left(\frac{13}{46}\right) e(2146)e\left(\frac{21}{46}\right) e(923)e\left(\frac{9}{23}\right) e(723)e\left(\frac{7}{23}\right) e(746)e\left(\frac{7}{46}\right) e(723)e\left(\frac{7}{23}\right)
χ967(326,⋅)\chi_{967}(326,\cdot) −1-1 11 e(123)e\left(\frac{1}{23}\right) e(3346)e\left(\frac{33}{46}\right) e(223)e\left(\frac{2}{23}\right) e(3146)e\left(\frac{31}{46}\right) e(3546)e\left(\frac{35}{46}\right) e(746)e\left(\frac{7}{46}\right) e(323)e\left(\frac{3}{23}\right) e(1023)e\left(\frac{10}{23}\right) e(3346)e\left(\frac{33}{46}\right) e(1023)e\left(\frac{10}{23}\right)
χ967(393,⋅)\chi_{967}(393,\cdot) −1-1 11 e(923)e\left(\frac{9}{23}\right) e(2146)e\left(\frac{21}{46}\right) e(1823)e\left(\frac{18}{23}\right) e(346)e\left(\frac{3}{46}\right) e(3946)e\left(\frac{39}{46}\right) e(1746)e\left(\frac{17}{46}\right) e(423)e\left(\frac{4}{23}\right) e(2123)e\left(\frac{21}{23}\right) e(2146)e\left(\frac{21}{46}\right) e(2123)e\left(\frac{21}{23}\right)
χ967(493,⋅)\chi_{967}(493,\cdot) −1-1 11 e(1023)e\left(\frac{10}{23}\right) e(3146)e\left(\frac{31}{46}\right) e(2023)e\left(\frac{20}{23}\right) e(1146)e\left(\frac{11}{46}\right) e(546)e\left(\frac{5}{46}\right) e(146)e\left(\frac{1}{46}\right) e(723)e\left(\frac{7}{23}\right) e(823)e\left(\frac{8}{23}\right) e(3146)e\left(\frac{31}{46}\right) e(823)e\left(\frac{8}{23}\right)
χ967(618,⋅)\chi_{967}(618,\cdot) −1-1 11 e(1923)e\left(\frac{19}{23}\right) e(2946)e\left(\frac{29}{46}\right) e(1523)e\left(\frac{15}{23}\right) e(3746)e\left(\frac{37}{46}\right) e(2146)e\left(\frac{21}{46}\right) e(4146)e\left(\frac{41}{46}\right) e(1123)e\left(\frac{11}{23}\right) e(623)e\left(\frac{6}{23}\right) e(2946)e\left(\frac{29}{46}\right) e(623)e\left(\frac{6}{23}\right)
χ967(635,⋅)\chi_{967}(635,\cdot) −1-1 11 e(2023)e\left(\frac{20}{23}\right) e(3946)e\left(\frac{39}{46}\right) e(1723)e\left(\frac{17}{23}\right) e(4546)e\left(\frac{45}{46}\right) e(3346)e\left(\frac{33}{46}\right) e(2546)e\left(\frac{25}{46}\right) e(1423)e\left(\frac{14}{23}\right) e(1623)e\left(\frac{16}{23}\right) e(3946)e\left(\frac{39}{46}\right) e(1623)e\left(\frac{16}{23}\right)
χ967(684,⋅)\chi_{967}(684,\cdot) −1-1 11 e(823)e\left(\frac{8}{23}\right) e(1146)e\left(\frac{11}{46}\right) e(1623)e\left(\frac{16}{23}\right) e(4146)e\left(\frac{41}{46}\right) e(2746)e\left(\frac{27}{46}\right) e(3346)e\left(\frac{33}{46}\right) e(123)e\left(\frac{1}{23}\right) e(1123)e\left(\frac{11}{23}\right) e(1146)e\left(\frac{11}{46}\right) e(1123)e\left(\frac{11}{23}\right)
χ967(771,⋅)\chi_{967}(771,\cdot) −1-1 11 e(1123)e\left(\frac{11}{23}\right) e(4146)e\left(\frac{41}{46}\right) e(2223)e\left(\frac{22}{23}\right) e(1946)e\left(\frac{19}{46}\right) e(1746)e\left(\frac{17}{46}\right) e(3146)e\left(\frac{31}{46}\right) e(1023)e\left(\frac{10}{23}\right) e(1823)e\left(\frac{18}{23}\right) e(4146)e\left(\frac{41}{46}\right) e(1823)e\left(\frac{18}{23}\right)
χ967(780,⋅)\chi_{967}(780,\cdot) −1-1 11 e(1423)e\left(\frac{14}{23}\right) e(2546)e\left(\frac{25}{46}\right) e(523)e\left(\frac{5}{23}\right) e(4346)e\left(\frac{43}{46}\right) e(746)e\left(\frac{7}{46}\right) e(2946)e\left(\frac{29}{46}\right) e(1923)e\left(\frac{19}{23}\right) e(223)e\left(\frac{2}{23}\right) e(2546)e\left(\frac{25}{46}\right) e(223)e\left(\frac{2}{23}\right)
χ967(810,⋅)\chi_{967}(810,\cdot) −1-1 11 e(523)e\left(\frac{5}{23}\right) e(2746)e\left(\frac{27}{46}\right) e(1023)e\left(\frac{10}{23}\right) e(1746)e\left(\frac{17}{46}\right) e(3746)e\left(\frac{37}{46}\right) e(3546)e\left(\frac{35}{46}\right) e(1523)e\left(\frac{15}{23}\right) e(423)e\left(\frac{4}{23}\right) e(2746)e\left(\frac{27}{46}\right) e(423)e\left(\frac{4}{23}\right)
χ967(834,⋅)\chi_{967}(834,\cdot) −1-1 11 e(423)e\left(\frac{4}{23}\right) e(1746)e\left(\frac{17}{46}\right) e(823)e\left(\frac{8}{23}\right) e(946)e\left(\frac{9}{46}\right) e(2546)e\left(\frac{25}{46}\right) e(546)e\left(\frac{5}{46}\right) e(1223)e\left(\frac{12}{23}\right) e(1723)e\left(\frac{17}{23}\right) e(1746)e\left(\frac{17}{46}\right) e(1723)e\left(\frac{17}{23}\right)
χ967(895,⋅)\chi_{967}(895,\cdot) −1-1 11 e(2123)e\left(\frac{21}{23}\right) e(346)e\left(\frac{3}{46}\right) e(1923)e\left(\frac{19}{23}\right) e(746)e\left(\frac{7}{46}\right) e(4546)e\left(\frac{45}{46}\right) e(946)e\left(\frac{9}{46}\right) e(1723)e\left(\frac{17}{23}\right) e(323)e\left(\frac{3}{23}\right) e(346)e\left(\frac{3}{46}\right) e(323)e\left(\frac{3}{23}\right)
χ967(898,⋅)\chi_{967}(898,\cdot) −1-1 11 e(623)e\left(\frac{6}{23}\right) e(3746)e\left(\frac{37}{46}\right) e(1223)e\left(\frac{12}{23}\right) e(2546)e\left(\frac{25}{46}\right) e(346)e\left(\frac{3}{46}\right) e(1946)e\left(\frac{19}{46}\right) e(1823)e\left(\frac{18}{23}\right) e(1423)e\left(\frac{14}{23}\right) e(3746)e\left(\frac{37}{46}\right) e(1423)e\left(\frac{14}{23}\right)