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Properties

Label 1183.bj
Modulus 11831183
Conductor 11831183
Order 3939
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(78))
 
M = H._module
 
chi = DirichletCharacter(H, M([26,46]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,1183))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 11831183
Conductor: 11831183
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3939
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(ζ39)\Q(\zeta_{39})
Fixed field: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1

Characters in Galois orbit

Character −1-1 11 22 33 44 55 66 88 99 1010 1111 1212
χ1183(9,⋅)\chi_{1183}(9,\cdot) 11 11 e(1039)e\left(\frac{10}{39}\right) e(613)e\left(\frac{6}{13}\right) e(2039)e\left(\frac{20}{39}\right) e(3839)e\left(\frac{38}{39}\right) e(2839)e\left(\frac{28}{39}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(3839)e\left(\frac{38}{39}\right)
χ1183(81,⋅)\chi_{1183}(81,\cdot) 11 11 e(2039)e\left(\frac{20}{39}\right) e(1213)e\left(\frac{12}{13}\right) e(139)e\left(\frac{1}{39}\right) e(3739)e\left(\frac{37}{39}\right) e(1739)e\left(\frac{17}{39}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(3739)e\left(\frac{37}{39}\right)
χ1183(100,⋅)\chi_{1183}(100,\cdot) 11 11 e(3139)e\left(\frac{31}{39}\right) e(313)e\left(\frac{3}{13}\right) e(2339)e\left(\frac{23}{39}\right) e(3239)e\left(\frac{32}{39}\right) e(139)e\left(\frac{1}{39}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(3239)e\left(\frac{32}{39}\right)
χ1183(172,⋅)\chi_{1183}(172,\cdot) 11 11 e(539)e\left(\frac{5}{39}\right) e(313)e\left(\frac{3}{13}\right) e(1039)e\left(\frac{10}{39}\right) e(1939)e\left(\frac{19}{39}\right) e(1439)e\left(\frac{14}{39}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1939)e\left(\frac{19}{39}\right)
χ1183(263,⋅)\chi_{1183}(263,\cdot) 11 11 e(2939)e\left(\frac{29}{39}\right) e(713)e\left(\frac{7}{13}\right) e(1939)e\left(\frac{19}{39}\right) e(139)e\left(\frac{1}{39}\right) e(1139)e\left(\frac{11}{39}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(139)e\left(\frac{1}{39}\right)
χ1183(282,⋅)\chi_{1183}(282,\cdot) 11 11 e(3439)e\left(\frac{34}{39}\right) e(1013)e\left(\frac{10}{13}\right) e(2939)e\left(\frac{29}{39}\right) e(2039)e\left(\frac{20}{39}\right) e(2539)e\left(\frac{25}{39}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(2039)e\left(\frac{20}{39}\right)
χ1183(354,⋅)\chi_{1183}(354,\cdot) 11 11 e(1439)e\left(\frac{14}{39}\right) e(1113)e\left(\frac{11}{13}\right) e(2839)e\left(\frac{28}{39}\right) e(2239)e\left(\frac{22}{39}\right) e(839)e\left(\frac{8}{39}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(2239)e\left(\frac{22}{39}\right)
χ1183(373,⋅)\chi_{1183}(373,\cdot) 11 11 e(1639)e\left(\frac{16}{39}\right) e(713)e\left(\frac{7}{13}\right) e(3239)e\left(\frac{32}{39}\right) e(1439)e\left(\frac{14}{39}\right) e(3739)e\left(\frac{37}{39}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(1439)e\left(\frac{14}{39}\right)
χ1183(445,⋅)\chi_{1183}(445,\cdot) 11 11 e(3839)e\left(\frac{38}{39}\right) e(213)e\left(\frac{2}{13}\right) e(3739)e\left(\frac{37}{39}\right) e(439)e\left(\frac{4}{39}\right) e(539)e\left(\frac{5}{39}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(439)e\left(\frac{4}{39}\right)
χ1183(464,⋅)\chi_{1183}(464,\cdot) 11 11 e(3739)e\left(\frac{37}{39}\right) e(413)e\left(\frac{4}{13}\right) e(3539)e\left(\frac{35}{39}\right) e(839)e\left(\frac{8}{39}\right) e(1039)e\left(\frac{10}{39}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(839)e\left(\frac{8}{39}\right)
χ1183(536,⋅)\chi_{1183}(536,\cdot) 11 11 e(2339)e\left(\frac{23}{39}\right) e(613)e\left(\frac{6}{13}\right) e(739)e\left(\frac{7}{39}\right) e(2539)e\left(\frac{25}{39}\right) e(239)e\left(\frac{2}{39}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(2539)e\left(\frac{25}{39}\right)
χ1183(555,⋅)\chi_{1183}(555,\cdot) 11 11 e(1939)e\left(\frac{19}{39}\right) e(113)e\left(\frac{1}{13}\right) e(3839)e\left(\frac{38}{39}\right) e(239)e\left(\frac{2}{39}\right) e(2239)e\left(\frac{22}{39}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(239)e\left(\frac{2}{39}\right)
χ1183(627,⋅)\chi_{1183}(627,\cdot) 11 11 e(839)e\left(\frac{8}{39}\right) e(1013)e\left(\frac{10}{13}\right) e(1639)e\left(\frac{16}{39}\right) e(739)e\left(\frac{7}{39}\right) e(3839)e\left(\frac{38}{39}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(739)e\left(\frac{7}{39}\right)
χ1183(646,⋅)\chi_{1183}(646,\cdot) 11 11 e(139)e\left(\frac{1}{39}\right) e(1113)e\left(\frac{11}{13}\right) e(239)e\left(\frac{2}{39}\right) e(3539)e\left(\frac{35}{39}\right) e(3439)e\left(\frac{34}{39}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(3539)e\left(\frac{35}{39}\right)
χ1183(718,⋅)\chi_{1183}(718,\cdot) 11 11 e(3239)e\left(\frac{32}{39}\right) e(113)e\left(\frac{1}{13}\right) e(2539)e\left(\frac{25}{39}\right) e(2839)e\left(\frac{28}{39}\right) e(3539)e\left(\frac{35}{39}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(2839)e\left(\frac{28}{39}\right)
χ1183(737,⋅)\chi_{1183}(737,\cdot) 11 11 e(2239)e\left(\frac{22}{39}\right) e(813)e\left(\frac{8}{13}\right) e(539)e\left(\frac{5}{39}\right) e(2939)e\left(\frac{29}{39}\right) e(739)e\left(\frac{7}{39}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(2939)e\left(\frac{29}{39}\right)
χ1183(809,⋅)\chi_{1183}(809,\cdot) 11 11 e(1739)e\left(\frac{17}{39}\right) e(513)e\left(\frac{5}{13}\right) e(3439)e\left(\frac{34}{39}\right) e(1039)e\left(\frac{10}{39}\right) e(3239)e\left(\frac{32}{39}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(1039)e\left(\frac{10}{39}\right)
χ1183(828,⋅)\chi_{1183}(828,\cdot) 11 11 e(439)e\left(\frac{4}{39}\right) e(513)e\left(\frac{5}{13}\right) e(839)e\left(\frac{8}{39}\right) e(2339)e\left(\frac{23}{39}\right) e(1939)e\left(\frac{19}{39}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(2339)e\left(\frac{23}{39}\right)
χ1183(900,⋅)\chi_{1183}(900,\cdot) 11 11 e(239)e\left(\frac{2}{39}\right) e(913)e\left(\frac{9}{13}\right) e(439)e\left(\frac{4}{39}\right) e(3139)e\left(\frac{31}{39}\right) e(2939)e\left(\frac{29}{39}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(3139)e\left(\frac{31}{39}\right)
χ1183(919,⋅)\chi_{1183}(919,\cdot) 11 11 e(2539)e\left(\frac{25}{39}\right) e(213)e\left(\frac{2}{13}\right) e(1139)e\left(\frac{11}{39}\right) e(1739)e\left(\frac{17}{39}\right) e(3139)e\left(\frac{31}{39}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1739)e\left(\frac{17}{39}\right)
χ1183(1010,⋅)\chi_{1183}(1010,\cdot) 11 11 e(739)e\left(\frac{7}{39}\right) e(1213)e\left(\frac{12}{13}\right) e(1439)e\left(\frac{14}{39}\right) e(1139)e\left(\frac{11}{39}\right) e(439)e\left(\frac{4}{39}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(1139)e\left(\frac{11}{39}\right)
χ1183(1082,⋅)\chi_{1183}(1082,\cdot) 11 11 e(1139)e\left(\frac{11}{39}\right) e(413)e\left(\frac{4}{13}\right) e(2239)e\left(\frac{22}{39}\right) e(3439)e\left(\frac{34}{39}\right) e(2339)e\left(\frac{23}{39}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(3439)e\left(\frac{34}{39}\right)
χ1183(1101,⋅)\chi_{1183}(1101,\cdot) 11 11 e(2839)e\left(\frac{28}{39}\right) e(913)e\left(\frac{9}{13}\right) e(1739)e\left(\frac{17}{39}\right) e(539)e\left(\frac{5}{39}\right) e(1639)e\left(\frac{16}{39}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(539)e\left(\frac{5}{39}\right)
χ1183(1173,⋅)\chi_{1183}(1173,\cdot) 11 11 e(3539)e\left(\frac{35}{39}\right) e(813)e\left(\frac{8}{13}\right) e(3139)e\left(\frac{31}{39}\right) e(1639)e\left(\frac{16}{39}\right) e(2039)e\left(\frac{20}{39}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(1639)e\left(\frac{16}{39}\right)