↑

Properties

Label 1911.dc
Modulus 19111911
Conductor 19111911
Order 4242
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1911, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([21,9,28]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(230,1911))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 19111911
Conductor: 19111911
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4242
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(ζ21)\Q(\zeta_{21})
Fixed field: Number field defined by a degree 42 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 55 88 1010 1111 1616 1717 1919 2020
χ1911(230,⋅)\chi_{1911}(230,\cdot) 11 11 e(3142)e\left(\frac{31}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(57)e\left(\frac{5}{7}\right) e(314)e\left(\frac{3}{14}\right) e(1942)e\left(\frac{19}{42}\right) e(3142)e\left(\frac{31}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(421)e\left(\frac{4}{21}\right) e(56)e\left(\frac{5}{6}\right) e(421)e\left(\frac{4}{21}\right)
χ1911(419,⋅)\chi_{1911}(419,\cdot) 11 11 e(2942)e\left(\frac{29}{42}\right) e(821)e\left(\frac{8}{21}\right) e(47)e\left(\frac{4}{7}\right) e(114)e\left(\frac{1}{14}\right) e(1142)e\left(\frac{11}{42}\right) e(2942)e\left(\frac{29}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(16)e\left(\frac{1}{6}\right) e(2021)e\left(\frac{20}{21}\right)
χ1911(503,⋅)\chi_{1911}(503,\cdot) 11 11 e(2542)e\left(\frac{25}{42}\right) e(421)e\left(\frac{4}{21}\right) e(27)e\left(\frac{2}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(3742)e\left(\frac{37}{42}\right) e(2542)e\left(\frac{25}{42}\right) e(821)e\left(\frac{8}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1021)e\left(\frac{10}{21}\right)
χ1911(692,⋅)\chi_{1911}(692,\cdot) 11 11 e(2342)e\left(\frac{23}{42}\right) e(221)e\left(\frac{2}{21}\right) e(17)e\left(\frac{1}{7}\right) e(914)e\left(\frac{9}{14}\right) e(2942)e\left(\frac{29}{42}\right) e(2342)e\left(\frac{23}{42}\right) e(421)e\left(\frac{4}{21}\right) e(521)e\left(\frac{5}{21}\right) e(16)e\left(\frac{1}{6}\right) e(521)e\left(\frac{5}{21}\right)
χ1911(776,⋅)\chi_{1911}(776,\cdot) 11 11 e(1942)e\left(\frac{19}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(67)e\left(\frac{6}{7}\right) e(514)e\left(\frac{5}{14}\right) e(1342)e\left(\frac{13}{42}\right) e(1942)e\left(\frac{19}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1621)e\left(\frac{16}{21}\right)
χ1911(965,⋅)\chi_{1911}(965,\cdot) 11 11 e(1742)e\left(\frac{17}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(57)e\left(\frac{5}{7}\right) e(314)e\left(\frac{3}{14}\right) e(542)e\left(\frac{5}{42}\right) e(1742)e\left(\frac{17}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(16)e\left(\frac{1}{6}\right) e(1121)e\left(\frac{11}{21}\right)
χ1911(1049,⋅)\chi_{1911}(1049,\cdot) 11 11 e(1342)e\left(\frac{13}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(3142)e\left(\frac{31}{42}\right) e(1342)e\left(\frac{13}{42}\right) e(521)e\left(\frac{5}{21}\right) e(121)e\left(\frac{1}{21}\right) e(56)e\left(\frac{5}{6}\right) e(121)e\left(\frac{1}{21}\right)
χ1911(1238,⋅)\chi_{1911}(1238,\cdot) 11 11 e(1142)e\left(\frac{11}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(27)e\left(\frac{2}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(2342)e\left(\frac{23}{42}\right) e(1142)e\left(\frac{11}{42}\right) e(121)e\left(\frac{1}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(16)e\left(\frac{1}{6}\right) e(1721)e\left(\frac{17}{21}\right)
χ1911(1511,⋅)\chi_{1911}(1511,\cdot) 11 11 e(542)e\left(\frac{5}{42}\right) e(521)e\left(\frac{5}{21}\right) e(67)e\left(\frac{6}{7}\right) e(514)e\left(\frac{5}{14}\right) e(4142)e\left(\frac{41}{42}\right) e(542)e\left(\frac{5}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(221)e\left(\frac{2}{21}\right) e(16)e\left(\frac{1}{6}\right) e(221)e\left(\frac{2}{21}\right)
χ1911(1595,⋅)\chi_{1911}(1595,\cdot) 11 11 e(142)e\left(\frac{1}{42}\right) e(121)e\left(\frac{1}{21}\right) e(47)e\left(\frac{4}{7}\right) e(114)e\left(\frac{1}{14}\right) e(2542)e\left(\frac{25}{42}\right) e(142)e\left(\frac{1}{42}\right) e(221)e\left(\frac{2}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1321)e\left(\frac{13}{21}\right)
χ1911(1784,⋅)\chi_{1911}(1784,\cdot) 11 11 e(4142)e\left(\frac{41}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(1742)e\left(\frac{17}{42}\right) e(4142)e\left(\frac{41}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(821)e\left(\frac{8}{21}\right) e(16)e\left(\frac{1}{6}\right) e(821)e\left(\frac{8}{21}\right)
χ1911(1868,⋅)\chi_{1911}(1868,\cdot) 11 11 e(3742)e\left(\frac{37}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(17)e\left(\frac{1}{7}\right) e(914)e\left(\frac{9}{14}\right) e(142)e\left(\frac{1}{42}\right) e(3742)e\left(\frac{37}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1921)e\left(\frac{19}{21}\right)