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Properties

Label 931.bt
Modulus 931931
Conductor 931931
Order 4242
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(931, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([17,21]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(75,931))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 931931
Conductor: 931931
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 33 44 55 66 88 99 1010 1111 1212
χ931(75,⋅)\chi_{931}(75,\cdot) 11 11 e(142)e\left(\frac{1}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(121)e\left(\frac{1}{21}\right) e(3142)e\left(\frac{31}{42}\right) e(1314)e\left(\frac{13}{14}\right) e(114)e\left(\frac{1}{14}\right) e(1721)e\left(\frac{17}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(421)e\left(\frac{4}{21}\right) e(2021)e\left(\frac{20}{21}\right)
χ931(94,⋅)\chi_{931}(94,\cdot) 11 11 e(2942)e\left(\frac{29}{42}\right) e(521)e\left(\frac{5}{21}\right) e(821)e\left(\frac{8}{21}\right) e(1742)e\left(\frac{17}{42}\right) e(1314)e\left(\frac{13}{14}\right) e(114)e\left(\frac{1}{14}\right) e(1021)e\left(\frac{10}{21}\right) e(221)e\left(\frac{2}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(1321)e\left(\frac{13}{21}\right)
χ931(208,⋅)\chi_{931}(208,\cdot) 11 11 e(1342)e\left(\frac{13}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(2542)e\left(\frac{25}{42}\right) e(114)e\left(\frac{1}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(1121)e\left(\frac{11}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(821)e\left(\frac{8}{21}\right)
χ931(341,⋅)\chi_{931}(341,\cdot) 11 11 e(2542)e\left(\frac{25}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(421)e\left(\frac{4}{21}\right) e(1942)e\left(\frac{19}{42}\right) e(314)e\left(\frac{3}{14}\right) e(1114)e\left(\frac{11}{14}\right) e(521)e\left(\frac{5}{21}\right) e(121)e\left(\frac{1}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(1721)e\left(\frac{17}{21}\right)
χ931(360,⋅)\chi_{931}(360,\cdot) 11 11 e(4142)e\left(\frac{41}{42}\right) e(221)e\left(\frac{2}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(1142)e\left(\frac{11}{42}\right) e(114)e\left(\frac{1}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(421)e\left(\frac{4}{21}\right) e(521)e\left(\frac{5}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(121)e\left(\frac{1}{21}\right)
χ931(474,⋅)\chi_{931}(474,\cdot) 11 11 e(3742)e\left(\frac{37}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(1342)e\left(\frac{13}{42}\right) e(514)e\left(\frac{5}{14}\right) e(914)e\left(\frac{9}{14}\right) e(2021)e\left(\frac{20}{21}\right) e(421)e\left(\frac{4}{21}\right) e(121)e\left(\frac{1}{21}\right) e(521)e\left(\frac{5}{21}\right)
χ931(493,⋅)\chi_{931}(493,\cdot) 11 11 e(542)e\left(\frac{5}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(521)e\left(\frac{5}{21}\right) e(2942)e\left(\frac{29}{42}\right) e(914)e\left(\frac{9}{14}\right) e(514)e\left(\frac{5}{14}\right) e(121)e\left(\frac{1}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(1621)e\left(\frac{16}{21}\right)
χ931(626,⋅)\chi_{931}(626,\cdot) 11 11 e(1142)e\left(\frac{11}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(542)e\left(\frac{5}{42}\right) e(314)e\left(\frac{3}{14}\right) e(1114)e\left(\frac{11}{14}\right) e(1921)e\left(\frac{19}{21}\right) e(821)e\left(\frac{8}{21}\right) e(221)e\left(\frac{2}{21}\right) e(1021)e\left(\frac{10}{21}\right)
χ931(740,⋅)\chi_{931}(740,\cdot) 11 11 e(1942)e\left(\frac{19}{42}\right) e(421)e\left(\frac{4}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(142)e\left(\frac{1}{42}\right) e(914)e\left(\frac{9}{14}\right) e(514)e\left(\frac{5}{14}\right) e(821)e\left(\frac{8}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(221)e\left(\frac{2}{21}\right)
χ931(759,⋅)\chi_{931}(759,\cdot) 11 11 e(1742)e\left(\frac{17}{42}\right) e(821)e\left(\frac{8}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(2342)e\left(\frac{23}{42}\right) e(1114)e\left(\frac{11}{14}\right) e(314)e\left(\frac{3}{14}\right) e(1621)e\left(\frac{16}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(521)e\left(\frac{5}{21}\right) e(421)e\left(\frac{4}{21}\right)
χ931(873,⋅)\chi_{931}(873,\cdot) 11 11 e(3142)e\left(\frac{31}{42}\right) e(121)e\left(\frac{1}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(3742)e\left(\frac{37}{42}\right) e(1114)e\left(\frac{11}{14}\right) e(314)e\left(\frac{3}{14}\right) e(221)e\left(\frac{2}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(1121)e\left(\frac{11}{21}\right)
χ931(892,⋅)\chi_{931}(892,\cdot) 11 11 e(2342)e\left(\frac{23}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(221)e\left(\frac{2}{21}\right) e(4142)e\left(\frac{41}{42}\right) e(514)e\left(\frac{5}{14}\right) e(914)e\left(\frac{9}{14}\right) e(1321)e\left(\frac{13}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(821)e\left(\frac{8}{21}\right) e(1921)e\left(\frac{19}{21}\right)