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Properties

Label 5733.km
Modulus 57335733
Conductor 57335733
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(5733, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([28,16,21]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(25,5733))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 57335733
Conductor: 57335733
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
χ5733(25,⋅)\chi_{5733}(25,\cdot) 11 11 e(114)e\left(\frac{1}{14}\right) e(17)e\left(\frac{1}{7}\right) e(3742)e\left(\frac{37}{42}\right) e(314)e\left(\frac{3}{14}\right) e(2021)e\left(\frac{20}{21}\right) e(1742)e\left(\frac{17}{42}\right) e(27)e\left(\frac{2}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(56)e\left(\frac{5}{6}\right) e(142)e\left(\frac{1}{42}\right)
χ5733(688,⋅)\chi_{5733}(688,\cdot) 11 11 e(1314)e\left(\frac{13}{14}\right) e(67)e\left(\frac{6}{7}\right) e(542)e\left(\frac{5}{42}\right) e(1114)e\left(\frac{11}{14}\right) e(121)e\left(\frac{1}{21}\right) e(2542)e\left(\frac{25}{42}\right) e(57)e\left(\frac{5}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(16)e\left(\frac{1}{6}\right) e(4142)e\left(\frac{41}{42}\right)
χ5733(844,⋅)\chi_{5733}(844,\cdot) 11 11 e(1314)e\left(\frac{13}{14}\right) e(67)e\left(\frac{6}{7}\right) e(1942)e\left(\frac{19}{42}\right) e(1114)e\left(\frac{11}{14}\right) e(821)e\left(\frac{8}{21}\right) e(1142)e\left(\frac{11}{42}\right) e(57)e\left(\frac{5}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1342)e\left(\frac{13}{42}\right)
χ5733(1507,⋅)\chi_{5733}(1507,\cdot) 11 11 e(914)e\left(\frac{9}{14}\right) e(27)e\left(\frac{2}{7}\right) e(1142)e\left(\frac{11}{42}\right) e(1314)e\left(\frac{13}{14}\right) e(1921)e\left(\frac{19}{21}\right) e(1342)e\left(\frac{13}{42}\right) e(47)e\left(\frac{4}{7}\right) e(121)e\left(\frac{1}{21}\right) e(16)e\left(\frac{1}{6}\right) e(2342)e\left(\frac{23}{42}\right)
χ5733(1663,⋅)\chi_{5733}(1663,\cdot) 11 11 e(1114)e\left(\frac{11}{14}\right) e(47)e\left(\frac{4}{7}\right) e(142)e\left(\frac{1}{42}\right) e(514)e\left(\frac{5}{14}\right) e(1721)e\left(\frac{17}{21}\right) e(542)e\left(\frac{5}{42}\right) e(17)e\left(\frac{1}{7}\right) e(221)e\left(\frac{2}{21}\right) e(56)e\left(\frac{5}{6}\right) e(2542)e\left(\frac{25}{42}\right)
χ5733(2326,⋅)\chi_{5733}(2326,\cdot) 11 11 e(514)e\left(\frac{5}{14}\right) e(57)e\left(\frac{5}{7}\right) e(1742)e\left(\frac{17}{42}\right) e(114)e\left(\frac{1}{14}\right) e(1621)e\left(\frac{16}{21}\right) e(142)e\left(\frac{1}{42}\right) e(37)e\left(\frac{3}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(16)e\left(\frac{1}{6}\right) e(542)e\left(\frac{5}{42}\right)
χ5733(2482,⋅)\chi_{5733}(2482,\cdot) 11 11 e(914)e\left(\frac{9}{14}\right) e(27)e\left(\frac{2}{7}\right) e(2542)e\left(\frac{25}{42}\right) e(1314)e\left(\frac{13}{14}\right) e(521)e\left(\frac{5}{21}\right) e(4142)e\left(\frac{41}{42}\right) e(47)e\left(\frac{4}{7}\right) e(821)e\left(\frac{8}{21}\right) e(56)e\left(\frac{5}{6}\right) e(3742)e\left(\frac{37}{42}\right)
χ5733(3145,⋅)\chi_{5733}(3145,\cdot) 11 11 e(114)e\left(\frac{1}{14}\right) e(17)e\left(\frac{1}{7}\right) e(2342)e\left(\frac{23}{42}\right) e(314)e\left(\frac{3}{14}\right) e(1321)e\left(\frac{13}{21}\right) e(3142)e\left(\frac{31}{42}\right) e(27)e\left(\frac{2}{7}\right) e(421)e\left(\frac{4}{21}\right) e(16)e\left(\frac{1}{6}\right) e(2942)e\left(\frac{29}{42}\right)
χ5733(3964,⋅)\chi_{5733}(3964,\cdot) 11 11 e(1114)e\left(\frac{11}{14}\right) e(47)e\left(\frac{4}{7}\right) e(2942)e\left(\frac{29}{42}\right) e(514)e\left(\frac{5}{14}\right) e(1021)e\left(\frac{10}{21}\right) e(1942)e\left(\frac{19}{42}\right) e(17)e\left(\frac{1}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(16)e\left(\frac{1}{6}\right) e(1142)e\left(\frac{11}{42}\right)
χ5733(4120,⋅)\chi_{5733}(4120,\cdot) 11 11 e(514)e\left(\frac{5}{14}\right) e(57)e\left(\frac{5}{7}\right) e(3142)e\left(\frac{31}{42}\right) e(114)e\left(\frac{1}{14}\right) e(221)e\left(\frac{2}{21}\right) e(2942)e\left(\frac{29}{42}\right) e(37)e\left(\frac{3}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(56)e\left(\frac{5}{6}\right) e(1942)e\left(\frac{19}{42}\right)
χ5733(4939,⋅)\chi_{5733}(4939,\cdot) 11 11 e(314)e\left(\frac{3}{14}\right) e(37)e\left(\frac{3}{7}\right) e(1342)e\left(\frac{13}{42}\right) e(914)e\left(\frac{9}{14}\right) e(1121)e\left(\frac{11}{21}\right) e(2342)e\left(\frac{23}{42}\right) e(67)e\left(\frac{6}{7}\right) e(521)e\left(\frac{5}{21}\right) e(56)e\left(\frac{5}{6}\right) e(3142)e\left(\frac{31}{42}\right)
χ5733(5602,⋅)\chi_{5733}(5602,\cdot) 11 11 e(314)e\left(\frac{3}{14}\right) e(37)e\left(\frac{3}{7}\right) e(4142)e\left(\frac{41}{42}\right) e(914)e\left(\frac{9}{14}\right) e(421)e\left(\frac{4}{21}\right) e(3742)e\left(\frac{37}{42}\right) e(67)e\left(\frac{6}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(16)e\left(\frac{1}{6}\right) e(1742)e\left(\frac{17}{42}\right)