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Properties

Label 760.cn
Modulus 760760
Conductor 760760
Order 3636
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(760, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([18,18,27,26]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(3,760))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 760760
Conductor: 760760
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3636
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(ζ36)\Q(\zeta_{36})
Fixed field: 36.0.4031181156993454136731178943694064571490658196389888000000000000000000000000000.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1717 2121 2323 2727 2929
χ760(3,⋅)\chi_{760}(3,\cdot) −1-1 11 e(2336)e\left(\frac{23}{36}\right) e(712)e\left(\frac{7}{12}\right) e(518)e\left(\frac{5}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1336)e\left(\frac{13}{36}\right) e(3536)e\left(\frac{35}{36}\right) e(29)e\left(\frac{2}{9}\right) e(736)e\left(\frac{7}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(518)e\left(\frac{5}{18}\right)
χ760(67,⋅)\chi_{760}(67,\cdot) −1-1 11 e(136)e\left(\frac{1}{36}\right) e(512)e\left(\frac{5}{12}\right) e(118)e\left(\frac{1}{18}\right) e(13)e\left(\frac{1}{3}\right) e(3536)e\left(\frac{35}{36}\right) e(2536)e\left(\frac{25}{36}\right) e(49)e\left(\frac{4}{9}\right) e(536)e\left(\frac{5}{36}\right) e(112)e\left(\frac{1}{12}\right) e(118)e\left(\frac{1}{18}\right)
χ760(147,⋅)\chi_{760}(147,\cdot) −1-1 11 e(2936)e\left(\frac{29}{36}\right) e(112)e\left(\frac{1}{12}\right) e(1118)e\left(\frac{11}{18}\right) e(23)e\left(\frac{2}{3}\right) e(736)e\left(\frac{7}{36}\right) e(536)e\left(\frac{5}{36}\right) e(89)e\left(\frac{8}{9}\right) e(136)e\left(\frac{1}{36}\right) e(512)e\left(\frac{5}{12}\right) e(1118)e\left(\frac{11}{18}\right)
χ760(203,⋅)\chi_{760}(203,\cdot) −1-1 11 e(3136)e\left(\frac{31}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(1318)e\left(\frac{13}{18}\right) e(13)e\left(\frac{1}{3}\right) e(536)e\left(\frac{5}{36}\right) e(1936)e\left(\frac{19}{36}\right) e(79)e\left(\frac{7}{9}\right) e(1136)e\left(\frac{11}{36}\right) e(712)e\left(\frac{7}{12}\right) e(1318)e\left(\frac{13}{18}\right)
χ760(243,⋅)\chi_{760}(243,\cdot) −1-1 11 e(736)e\left(\frac{7}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(718)e\left(\frac{7}{18}\right) e(13)e\left(\frac{1}{3}\right) e(2936)e\left(\frac{29}{36}\right) e(3136)e\left(\frac{31}{36}\right) e(19)e\left(\frac{1}{9}\right) e(3536)e\left(\frac{35}{36}\right) e(712)e\left(\frac{7}{12}\right) e(718)e\left(\frac{7}{18}\right)
χ760(307,⋅)\chi_{760}(307,\cdot) −1-1 11 e(536)e\left(\frac{5}{36}\right) e(112)e\left(\frac{1}{12}\right) e(518)e\left(\frac{5}{18}\right) e(23)e\left(\frac{2}{3}\right) e(3136)e\left(\frac{31}{36}\right) e(1736)e\left(\frac{17}{36}\right) e(29)e\left(\frac{2}{9}\right) e(2536)e\left(\frac{25}{36}\right) e(512)e\left(\frac{5}{12}\right) e(518)e\left(\frac{5}{18}\right)
χ760(363,⋅)\chi_{760}(363,\cdot) −1-1 11 e(3536)e\left(\frac{35}{36}\right) e(712)e\left(\frac{7}{12}\right) e(1718)e\left(\frac{17}{18}\right) e(23)e\left(\frac{2}{3}\right) e(136)e\left(\frac{1}{36}\right) e(1136)e\left(\frac{11}{36}\right) e(59)e\left(\frac{5}{9}\right) e(3136)e\left(\frac{31}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(1718)e\left(\frac{17}{18}\right)
χ760(507,⋅)\chi_{760}(507,\cdot) −1-1 11 e(1336)e\left(\frac{13}{36}\right) e(512)e\left(\frac{5}{12}\right) e(1318)e\left(\frac{13}{18}\right) e(13)e\left(\frac{1}{3}\right) e(2336)e\left(\frac{23}{36}\right) e(136)e\left(\frac{1}{36}\right) e(79)e\left(\frac{7}{9}\right) e(2936)e\left(\frac{29}{36}\right) e(112)e\left(\frac{1}{12}\right) e(1318)e\left(\frac{13}{18}\right)
χ760(523,⋅)\chi_{760}(523,\cdot) −1-1 11 e(1936)e\left(\frac{19}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(118)e\left(\frac{1}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1736)e\left(\frac{17}{36}\right) e(736)e\left(\frac{7}{36}\right) e(49)e\left(\frac{4}{9}\right) e(2336)e\left(\frac{23}{36}\right) e(712)e\left(\frac{7}{12}\right) e(118)e\left(\frac{1}{18}\right)
χ760(547,⋅)\chi_{760}(547,\cdot) −1-1 11 e(2536)e\left(\frac{25}{36}\right) e(512)e\left(\frac{5}{12}\right) e(718)e\left(\frac{7}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1136)e\left(\frac{11}{36}\right) e(1336)e\left(\frac{13}{36}\right) e(19)e\left(\frac{1}{9}\right) e(1736)e\left(\frac{17}{36}\right) e(112)e\left(\frac{1}{12}\right) e(718)e\left(\frac{7}{18}\right)
χ760(603,⋅)\chi_{760}(603,\cdot) −1-1 11 e(1136)e\left(\frac{11}{36}\right) e(712)e\left(\frac{7}{12}\right) e(1118)e\left(\frac{11}{18}\right) e(23)e\left(\frac{2}{3}\right) e(2536)e\left(\frac{25}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(89)e\left(\frac{8}{9}\right) e(1936)e\left(\frac{19}{36}\right) e(1112)e\left(\frac{11}{12}\right) e(1118)e\left(\frac{11}{18}\right)
χ760(667,⋅)\chi_{760}(667,\cdot) −1-1 11 e(1736)e\left(\frac{17}{36}\right) e(112)e\left(\frac{1}{12}\right) e(1718)e\left(\frac{17}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1936)e\left(\frac{19}{36}\right) e(2936)e\left(\frac{29}{36}\right) e(59)e\left(\frac{5}{9}\right) e(1336)e\left(\frac{13}{36}\right) e(512)e\left(\frac{5}{12}\right) e(1718)e\left(\frac{17}{18}\right)