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Properties

Label 2352.da
Modulus 23522352
Conductor 11761176
Order 4242
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2352, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,21,21,23]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(89,2352))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 23522352
Conductor: 11761176
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4242
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1176.cc
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ21)\Q(\zeta_{21})
Fixed field: 42.42.11402108177106104552822037830207017370882719938852769609842060849495301710065603498954056531968.1

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ2352(89,⋅)\chi_{2352}(89,\cdot) 11 11 e(3742)e\left(\frac{37}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(47)e\left(\frac{4}{7}\right) e(421)e\left(\frac{4}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1342)e\left(\frac{13}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(67)e\left(\frac{6}{7}\right) e(56)e\left(\frac{5}{6}\right) e(142)e\left(\frac{1}{42}\right)
χ2352(185,⋅)\chi_{2352}(185,\cdot) 11 11 e(542)e\left(\frac{5}{42}\right) e(221)e\left(\frac{2}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(13)e\left(\frac{1}{3}\right) e(2942)e\left(\frac{29}{42}\right) e(521)e\left(\frac{5}{21}\right) e(17)e\left(\frac{1}{7}\right) e(16)e\left(\frac{1}{6}\right) e(4142)e\left(\frac{41}{42}\right)
χ2352(425,⋅)\chi_{2352}(425,\cdot) 11 11 e(1342)e\left(\frac{13}{42}\right) e(121)e\left(\frac{1}{21}\right) e(57)e\left(\frac{5}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(23)e\left(\frac{2}{3}\right) e(2542)e\left(\frac{25}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(47)e\left(\frac{4}{7}\right) e(56)e\left(\frac{5}{6}\right) e(3142)e\left(\frac{31}{42}\right)
χ2352(761,⋅)\chi_{2352}(761,\cdot) 11 11 e(3142)e\left(\frac{31}{42}\right) e(421)e\left(\frac{4}{21}\right) e(67)e\left(\frac{6}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(23)e\left(\frac{2}{3}\right) e(3742)e\left(\frac{37}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(27)e\left(\frac{2}{7}\right) e(56)e\left(\frac{5}{6}\right) e(1942)e\left(\frac{19}{42}\right)
χ2352(857,⋅)\chi_{2352}(857,\cdot) 11 11 e(2342)e\left(\frac{23}{42}\right) e(521)e\left(\frac{5}{21}\right) e(47)e\left(\frac{4}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(13)e\left(\frac{1}{3}\right) e(4142)e\left(\frac{41}{42}\right) e(221)e\left(\frac{2}{21}\right) e(67)e\left(\frac{6}{7}\right) e(16)e\left(\frac{1}{6}\right) e(2942)e\left(\frac{29}{42}\right)
χ2352(1193,⋅)\chi_{2352}(1193,\cdot) 11 11 e(1142)e\left(\frac{11}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(17)e\left(\frac{1}{7}\right) e(821)e\left(\frac{8}{21}\right) e(13)e\left(\frac{1}{3}\right) e(542)e\left(\frac{5}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(57)e\left(\frac{5}{7}\right) e(16)e\left(\frac{1}{6}\right) e(2342)e\left(\frac{23}{42}\right)
χ2352(1433,⋅)\chi_{2352}(1433,\cdot) 11 11 e(2542)e\left(\frac{25}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(17)e\left(\frac{1}{7}\right) e(121)e\left(\frac{1}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1942)e\left(\frac{19}{42}\right) e(421)e\left(\frac{4}{21}\right) e(57)e\left(\frac{5}{7}\right) e(56)e\left(\frac{5}{6}\right) e(3742)e\left(\frac{37}{42}\right)
χ2352(1529,⋅)\chi_{2352}(1529,\cdot) 11 11 e(4142)e\left(\frac{41}{42}\right) e(821)e\left(\frac{8}{21}\right) e(57)e\left(\frac{5}{7}\right) e(521)e\left(\frac{5}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1142)e\left(\frac{11}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(47)e\left(\frac{4}{7}\right) e(16)e\left(\frac{1}{6}\right) e(1742)e\left(\frac{17}{42}\right)
χ2352(1769,⋅)\chi_{2352}(1769,\cdot) 11 11 e(142)e\left(\frac{1}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(27)e\left(\frac{2}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(23)e\left(\frac{2}{3}\right) e(3142)e\left(\frac{31}{42}\right) e(121)e\left(\frac{1}{21}\right) e(37)e\left(\frac{3}{7}\right) e(56)e\left(\frac{5}{6}\right) e(2542)e\left(\frac{25}{42}\right)
χ2352(1865,⋅)\chi_{2352}(1865,\cdot) 11 11 e(2942)e\left(\frac{29}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(27)e\left(\frac{2}{7}\right) e(221)e\left(\frac{2}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1742)e\left(\frac{17}{42}\right) e(821)e\left(\frac{8}{21}\right) e(37)e\left(\frac{3}{7}\right) e(16)e\left(\frac{1}{6}\right) e(1142)e\left(\frac{11}{42}\right)
χ2352(2105,⋅)\chi_{2352}(2105,\cdot) 11 11 e(1942)e\left(\frac{19}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(23)e\left(\frac{2}{3}\right) e(142)e\left(\frac{1}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(17)e\left(\frac{1}{7}\right) e(56)e\left(\frac{5}{6}\right) e(1342)e\left(\frac{13}{42}\right)
χ2352(2201,⋅)\chi_{2352}(2201,\cdot) 11 11 e(1742)e\left(\frac{17}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(67)e\left(\frac{6}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(13)e\left(\frac{1}{3}\right) e(2342)e\left(\frac{23}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(27)e\left(\frac{2}{7}\right) e(16)e\left(\frac{1}{6}\right) e(542)e\left(\frac{5}{42}\right)