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Properties

Label 3528.fx
Modulus 35283528
Conductor 35283528
Order 4242
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([21,21,28,32]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(331,3528))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 35283528
Conductor: 35283528
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: Number field defined by a degree 42 polynomial

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ3528(331,⋅)\chi_{3528}(331,\cdot) −1-1 11 e(1314)e\left(\frac{13}{14}\right) e(17)e\left(\frac{1}{7}\right) e(4142)e\left(\frac{41}{42}\right) e(121)e\left(\frac{1}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1114)e\left(\frac{11}{14}\right) e(67)e\left(\frac{6}{7}\right) e(3742)e\left(\frac{37}{42}\right) e(16)e\left(\frac{1}{6}\right) e(3742)e\left(\frac{37}{42}\right)
χ3528(571,⋅)\chi_{3528}(571,\cdot) −1-1 11 e(1314)e\left(\frac{13}{14}\right) e(17)e\left(\frac{1}{7}\right) e(1342)e\left(\frac{13}{42}\right) e(821)e\left(\frac{8}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1114)e\left(\frac{11}{14}\right) e(67)e\left(\frac{6}{7}\right) e(2342)e\left(\frac{23}{42}\right) e(56)e\left(\frac{5}{6}\right) e(2342)e\left(\frac{23}{42}\right)
χ3528(835,⋅)\chi_{3528}(835,\cdot) −1-1 11 e(1114)e\left(\frac{11}{14}\right) e(37)e\left(\frac{3}{7}\right) e(1142)e\left(\frac{11}{42}\right) e(1021)e\left(\frac{10}{21}\right) e(23)e\left(\frac{2}{3}\right) e(514)e\left(\frac{5}{14}\right) e(47)e\left(\frac{4}{7}\right) e(1342)e\left(\frac{13}{42}\right) e(16)e\left(\frac{1}{6}\right) e(1342)e\left(\frac{13}{42}\right)
χ3528(1075,⋅)\chi_{3528}(1075,\cdot) −1-1 11 e(514)e\left(\frac{5}{14}\right) e(27)e\left(\frac{2}{7}\right) e(1942)e\left(\frac{19}{42}\right) e(221)e\left(\frac{2}{21}\right) e(13)e\left(\frac{1}{3}\right) e(114)e\left(\frac{1}{14}\right) e(57)e\left(\frac{5}{7}\right) e(1142)e\left(\frac{11}{42}\right) e(56)e\left(\frac{5}{6}\right) e(1142)e\left(\frac{11}{42}\right)
χ3528(1339,⋅)\chi_{3528}(1339,\cdot) −1-1 11 e(914)e\left(\frac{9}{14}\right) e(57)e\left(\frac{5}{7}\right) e(2342)e\left(\frac{23}{42}\right) e(1921)e\left(\frac{19}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1314)e\left(\frac{13}{14}\right) e(27)e\left(\frac{2}{7}\right) e(3142)e\left(\frac{31}{42}\right) e(16)e\left(\frac{1}{6}\right) e(3142)e\left(\frac{31}{42}\right)
χ3528(1579,⋅)\chi_{3528}(1579,\cdot) −1-1 11 e(1114)e\left(\frac{11}{14}\right) e(37)e\left(\frac{3}{7}\right) e(2542)e\left(\frac{25}{42}\right) e(1721)e\left(\frac{17}{21}\right) e(13)e\left(\frac{1}{3}\right) e(514)e\left(\frac{5}{14}\right) e(47)e\left(\frac{4}{7}\right) e(4142)e\left(\frac{41}{42}\right) e(56)e\left(\frac{5}{6}\right) e(4142)e\left(\frac{41}{42}\right)
χ3528(2083,⋅)\chi_{3528}(2083,\cdot) −1-1 11 e(314)e\left(\frac{3}{14}\right) e(47)e\left(\frac{4}{7}\right) e(3142)e\left(\frac{31}{42}\right) e(1121)e\left(\frac{11}{21}\right) e(13)e\left(\frac{1}{3}\right) e(914)e\left(\frac{9}{14}\right) e(37)e\left(\frac{3}{7}\right) e(2942)e\left(\frac{29}{42}\right) e(56)e\left(\frac{5}{6}\right) e(2942)e\left(\frac{29}{42}\right)
χ3528(2347,⋅)\chi_{3528}(2347,\cdot) −1-1 11 e(514)e\left(\frac{5}{14}\right) e(27)e\left(\frac{2}{7}\right) e(542)e\left(\frac{5}{42}\right) e(1621)e\left(\frac{16}{21}\right) e(23)e\left(\frac{2}{3}\right) e(114)e\left(\frac{1}{14}\right) e(57)e\left(\frac{5}{7}\right) e(2542)e\left(\frac{25}{42}\right) e(16)e\left(\frac{1}{6}\right) e(2542)e\left(\frac{25}{42}\right)
χ3528(2587,⋅)\chi_{3528}(2587,\cdot) −1-1 11 e(914)e\left(\frac{9}{14}\right) e(57)e\left(\frac{5}{7}\right) e(3742)e\left(\frac{37}{42}\right) e(521)e\left(\frac{5}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1314)e\left(\frac{13}{14}\right) e(27)e\left(\frac{2}{7}\right) e(1742)e\left(\frac{17}{42}\right) e(56)e\left(\frac{5}{6}\right) e(1742)e\left(\frac{17}{42}\right)
χ3528(2851,⋅)\chi_{3528}(2851,\cdot) −1-1 11 e(314)e\left(\frac{3}{14}\right) e(47)e\left(\frac{4}{7}\right) e(1742)e\left(\frac{17}{42}\right) e(421)e\left(\frac{4}{21}\right) e(23)e\left(\frac{2}{3}\right) e(914)e\left(\frac{9}{14}\right) e(37)e\left(\frac{3}{7}\right) e(142)e\left(\frac{1}{42}\right) e(16)e\left(\frac{1}{6}\right) e(142)e\left(\frac{1}{42}\right)
χ3528(3091,⋅)\chi_{3528}(3091,\cdot) −1-1 11 e(114)e\left(\frac{1}{14}\right) e(67)e\left(\frac{6}{7}\right) e(142)e\left(\frac{1}{42}\right) e(2021)e\left(\frac{20}{21}\right) e(13)e\left(\frac{1}{3}\right) e(314)e\left(\frac{3}{14}\right) e(17)e\left(\frac{1}{7}\right) e(542)e\left(\frac{5}{42}\right) e(56)e\left(\frac{5}{6}\right) e(542)e\left(\frac{5}{42}\right)
χ3528(3355,⋅)\chi_{3528}(3355,\cdot) −1-1 11 e(114)e\left(\frac{1}{14}\right) e(67)e\left(\frac{6}{7}\right) e(2942)e\left(\frac{29}{42}\right) e(1321)e\left(\frac{13}{21}\right) e(23)e\left(\frac{2}{3}\right) e(314)e\left(\frac{3}{14}\right) e(17)e\left(\frac{1}{7}\right) e(1942)e\left(\frac{19}{42}\right) e(16)e\left(\frac{1}{6}\right) e(1942)e\left(\frac{19}{42}\right)