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Properties

Label 392.bf
Modulus 392392
Conductor 392392
Order 4242
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,21,29]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(5,392))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 392392
Conductor: 392392
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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ21)\Q(\zeta_{21})
Fixed field: 42.0.1090030896264192289800449659845679818091197961133776603876122561317234873686091104256.1

Characters in Galois orbit

Character −1-1 11 33 55 99 1111 1313 1515 1717 1919 2323 2525
χ392(5,⋅)\chi_{392}(5,\cdot) −1-1 11 e(421)e\left(\frac{4}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(821)e\left(\frac{8}{21}\right) e(542)e\left(\frac{5}{42}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(1142)e\left(\frac{11}{42}\right) e(23)e\left(\frac{2}{3}\right) e(521)e\left(\frac{5}{21}\right) e(121)e\left(\frac{1}{21}\right)
χ392(45,⋅)\chi_{392}(45,\cdot) −1-1 11 e(521)e\left(\frac{5}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(142)e\left(\frac{1}{42}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1942)e\left(\frac{19}{42}\right) e(13)e\left(\frac{1}{3}\right) e(121)e\left(\frac{1}{21}\right) e(1721)e\left(\frac{17}{21}\right)
χ392(61,⋅)\chi_{392}(61,\cdot) −1-1 11 e(1621)e\left(\frac{16}{21}\right) e(221)e\left(\frac{2}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(4142)e\left(\frac{41}{42}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(2342)e\left(\frac{23}{42}\right) e(23)e\left(\frac{2}{3}\right) e(2021)e\left(\frac{20}{21}\right) e(421)e\left(\frac{4}{21}\right)
χ392(101,⋅)\chi_{392}(101,\cdot) −1-1 11 e(1121)e\left(\frac{11}{21}\right) e(421)e\left(\frac{4}{21}\right) e(121)e\left(\frac{1}{21}\right) e(1942)e\left(\frac{19}{42}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(2542)e\left(\frac{25}{42}\right) e(13)e\left(\frac{1}{3}\right) e(1921)e\left(\frac{19}{21}\right) e(821)e\left(\frac{8}{21}\right)
χ392(157,⋅)\chi_{392}(157,\cdot) −1-1 11 e(1721)e\left(\frac{17}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(3742)e\left(\frac{37}{42}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(3142)e\left(\frac{31}{42}\right) e(13)e\left(\frac{1}{3}\right) e(1621)e\left(\frac{16}{21}\right) e(2021)e\left(\frac{20}{21}\right)
χ392(173,⋅)\chi_{392}(173,\cdot) −1-1 11 e(1921)e\left(\frac{19}{21}\right) e(521)e\left(\frac{5}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(2942)e\left(\frac{29}{42}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(542)e\left(\frac{5}{42}\right) e(23)e\left(\frac{2}{3}\right) e(821)e\left(\frac{8}{21}\right) e(1021)e\left(\frac{10}{21}\right)
χ392(213,⋅)\chi_{392}(213,\cdot) −1-1 11 e(221)e\left(\frac{2}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(421)e\left(\frac{4}{21}\right) e(1342)e\left(\frac{13}{42}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(3742)e\left(\frac{37}{42}\right) e(13)e\left(\frac{1}{3}\right) e(1321)e\left(\frac{13}{21}\right) e(1121)e\left(\frac{11}{21}\right)
χ392(229,⋅)\chi_{392}(229,\cdot) −1-1 11 e(1021)e\left(\frac{10}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(2342)e\left(\frac{23}{42}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1742)e\left(\frac{17}{42}\right) e(23)e\left(\frac{2}{3}\right) e(221)e\left(\frac{2}{21}\right) e(1321)e\left(\frac{13}{21}\right)
χ392(269,⋅)\chi_{392}(269,\cdot) −1-1 11 e(821)e\left(\frac{8}{21}\right) e(121)e\left(\frac{1}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(3142)e\left(\frac{31}{42}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(142)e\left(\frac{1}{42}\right) e(13)e\left(\frac{1}{3}\right) e(1021)e\left(\frac{10}{21}\right) e(221)e\left(\frac{2}{21}\right)
χ392(285,⋅)\chi_{392}(285,\cdot) −1-1 11 e(121)e\left(\frac{1}{21}\right) e(821)e\left(\frac{8}{21}\right) e(221)e\left(\frac{2}{21}\right) e(1742)e\left(\frac{17}{42}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(2942)e\left(\frac{29}{42}\right) e(23)e\left(\frac{2}{3}\right) e(1721)e\left(\frac{17}{21}\right) e(1621)e\left(\frac{16}{21}\right)
χ392(341,⋅)\chi_{392}(341,\cdot) −1-1 11 e(1321)e\left(\frac{13}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(521)e\left(\frac{5}{21}\right) e(1142)e\left(\frac{11}{42}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(4142)e\left(\frac{41}{42}\right) e(23)e\left(\frac{2}{3}\right) e(1121)e\left(\frac{11}{21}\right) e(1921)e\left(\frac{19}{21}\right)
χ392(381,⋅)\chi_{392}(381,\cdot) −1-1 11 e(2021)e\left(\frac{20}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(2542)e\left(\frac{25}{42}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1342)e\left(\frac{13}{42}\right) e(13)e\left(\frac{1}{3}\right) e(421)e\left(\frac{4}{21}\right) e(521)e\left(\frac{5}{21}\right)