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Properties

Label 1520.en
Modulus 15201520
Conductor 15201520
Order 3636
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(1520, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([18,9,18,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(59,1520))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 15201520
Conductor: 15201520
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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ36)\Q(\zeta_{36})
Fixed field: Number field defined by a degree 36 polynomial

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1717 2121 2323 2727 2929
χ1520(59,⋅)\chi_{1520}(59,\cdot) 11 11 e(1736)e\left(\frac{17}{36}\right) e(56)e\left(\frac{5}{6}\right) e(1718)e\left(\frac{17}{18}\right) e(512)e\left(\frac{5}{12}\right) e(1936)e\left(\frac{19}{36}\right) e(118)e\left(\frac{1}{18}\right) e(1136)e\left(\frac{11}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(512)e\left(\frac{5}{12}\right) e(2536)e\left(\frac{25}{36}\right)
χ1520(219,⋅)\chi_{1520}(219,\cdot) 11 11 e(136)e\left(\frac{1}{36}\right) e(16)e\left(\frac{1}{6}\right) e(118)e\left(\frac{1}{18}\right) e(112)e\left(\frac{1}{12}\right) e(3536)e\left(\frac{35}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(736)e\left(\frac{7}{36}\right) e(718)e\left(\frac{7}{18}\right) e(112)e\left(\frac{1}{12}\right) e(2936)e\left(\frac{29}{36}\right)
χ1520(299,⋅)\chi_{1520}(299,\cdot) 11 11 e(2936)e\left(\frac{29}{36}\right) e(56)e\left(\frac{5}{6}\right) e(1118)e\left(\frac{11}{18}\right) e(512)e\left(\frac{5}{12}\right) e(736)e\left(\frac{7}{36}\right) e(718)e\left(\frac{7}{18}\right) e(2336)e\left(\frac{23}{36}\right) e(518)e\left(\frac{5}{18}\right) e(512)e\left(\frac{5}{12}\right) e(1336)e\left(\frac{13}{36}\right)
χ1520(459,⋅)\chi_{1520}(459,\cdot) 11 11 e(536)e\left(\frac{5}{36}\right) e(56)e\left(\frac{5}{6}\right) e(518)e\left(\frac{5}{18}\right) e(512)e\left(\frac{5}{12}\right) e(3136)e\left(\frac{31}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(3536)e\left(\frac{35}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(512)e\left(\frac{5}{12}\right) e(136)e\left(\frac{1}{36}\right)
χ1520(659,⋅)\chi_{1520}(659,\cdot) 11 11 e(3136)e\left(\frac{31}{36}\right) e(16)e\left(\frac{1}{6}\right) e(1318)e\left(\frac{13}{18}\right) e(712)e\left(\frac{7}{12}\right) e(536)e\left(\frac{5}{36}\right) e(518)e\left(\frac{5}{18}\right) e(136)e\left(\frac{1}{36}\right) e(118)e\left(\frac{1}{18}\right) e(712)e\left(\frac{7}{12}\right) e(3536)e\left(\frac{35}{36}\right)
χ1520(699,⋅)\chi_{1520}(699,\cdot) 11 11 e(2536)e\left(\frac{25}{36}\right) e(16)e\left(\frac{1}{6}\right) e(718)e\left(\frac{7}{18}\right) e(112)e\left(\frac{1}{12}\right) e(1136)e\left(\frac{11}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(3136)e\left(\frac{31}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(112)e\left(\frac{1}{12}\right) e(536)e\left(\frac{5}{36}\right)
χ1520(819,⋅)\chi_{1520}(819,\cdot) 11 11 e(3536)e\left(\frac{35}{36}\right) e(56)e\left(\frac{5}{6}\right) e(1718)e\left(\frac{17}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(136)e\left(\frac{1}{36}\right) e(118)e\left(\frac{1}{18}\right) e(2936)e\left(\frac{29}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(736)e\left(\frac{7}{36}\right)
χ1520(979,⋅)\chi_{1520}(979,\cdot) 11 11 e(1936)e\left(\frac{19}{36}\right) e(16)e\left(\frac{1}{6}\right) e(118)e\left(\frac{1}{18}\right) e(712)e\left(\frac{7}{12}\right) e(1736)e\left(\frac{17}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(2536)e\left(\frac{25}{36}\right) e(718)e\left(\frac{7}{18}\right) e(712)e\left(\frac{7}{12}\right) e(1136)e\left(\frac{11}{36}\right)
χ1520(1059,⋅)\chi_{1520}(1059,\cdot) 11 11 e(1136)e\left(\frac{11}{36}\right) e(56)e\left(\frac{5}{6}\right) e(1118)e\left(\frac{11}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(2536)e\left(\frac{25}{36}\right) e(718)e\left(\frac{7}{18}\right) e(536)e\left(\frac{5}{36}\right) e(518)e\left(\frac{5}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(3136)e\left(\frac{31}{36}\right)
χ1520(1219,⋅)\chi_{1520}(1219,\cdot) 11 11 e(2336)e\left(\frac{23}{36}\right) e(56)e\left(\frac{5}{6}\right) e(518)e\left(\frac{5}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(1336)e\left(\frac{13}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(1736)e\left(\frac{17}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(1112)e\left(\frac{11}{12}\right) e(1936)e\left(\frac{19}{36}\right)
χ1520(1419,⋅)\chi_{1520}(1419,\cdot) 11 11 e(1336)e\left(\frac{13}{36}\right) e(16)e\left(\frac{1}{6}\right) e(1318)e\left(\frac{13}{18}\right) e(112)e\left(\frac{1}{12}\right) e(2336)e\left(\frac{23}{36}\right) e(518)e\left(\frac{5}{18}\right) e(1936)e\left(\frac{19}{36}\right) e(118)e\left(\frac{1}{18}\right) e(112)e\left(\frac{1}{12}\right) e(1736)e\left(\frac{17}{36}\right)
χ1520(1459,⋅)\chi_{1520}(1459,\cdot) 11 11 e(736)e\left(\frac{7}{36}\right) e(16)e\left(\frac{1}{6}\right) e(718)e\left(\frac{7}{18}\right) e(712)e\left(\frac{7}{12}\right) e(2936)e\left(\frac{29}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(1336)e\left(\frac{13}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(712)e\left(\frac{7}{12}\right) e(2336)e\left(\frac{23}{36}\right)