↑

Properties

Label 3528.ds
Modulus 35283528
Conductor 441441
Order 2121
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,14,22]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(193,3528))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 35283528
Conductor: 441441
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2121
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 441.z
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 21 polynomial

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ3528(193,⋅)\chi_{3528}(193,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(27)e\left(\frac{2}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(221)e\left(\frac{2}{21}\right) e(13)e\left(\frac{1}{3}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1621)e\left(\frac{16}{21}\right)
χ3528(457,⋅)\chi_{3528}(457,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(57)e\left(\frac{5}{7}\right) e(121)e\left(\frac{1}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(23)e\left(\frac{2}{3}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) e(521)e\left(\frac{5}{21}\right) e(23)e\left(\frac{2}{3}\right) e(521)e\left(\frac{5}{21}\right)
χ3528(697,⋅)\chi_{3528}(697,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(37)e\left(\frac{3}{7}\right) e(221)e\left(\frac{2}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(13)e\left(\frac{1}{3}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1021)e\left(\frac{10}{21}\right)
χ3528(1201,⋅)\chi_{3528}(1201,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(47)e\left(\frac{4}{7}\right) e(521)e\left(\frac{5}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(13)e\left(\frac{1}{3}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) e(421)e\left(\frac{4}{21}\right) e(13)e\left(\frac{1}{3}\right) e(421)e\left(\frac{4}{21}\right)
χ3528(1465,⋅)\chi_{3528}(1465,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(23)e\left(\frac{2}{3}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) e(221)e\left(\frac{2}{21}\right) e(23)e\left(\frac{2}{3}\right) e(221)e\left(\frac{2}{21}\right)
χ3528(1705,⋅)\chi_{3528}(1705,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(57)e\left(\frac{5}{7}\right) e(821)e\left(\frac{8}{21}\right) e(521)e\left(\frac{5}{21}\right) e(13)e\left(\frac{1}{3}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1921)e\left(\frac{19}{21}\right)
χ3528(1969,⋅)\chi_{3528}(1969,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(421)e\left(\frac{4}{21}\right) e(23)e\left(\frac{2}{3}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1121)e\left(\frac{11}{21}\right)
χ3528(2209,⋅)\chi_{3528}(2209,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(67)e\left(\frac{6}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(13)e\left(\frac{1}{3}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(13)e\left(\frac{1}{3}\right) e(1321)e\left(\frac{13}{21}\right)
χ3528(2473,⋅)\chi_{3528}(2473,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(67)e\left(\frac{6}{7}\right) e(421)e\left(\frac{4}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(23)e\left(\frac{2}{3}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(23)e\left(\frac{2}{3}\right) e(2021)e\left(\frac{20}{21}\right)
χ3528(2977,⋅)\chi_{3528}(2977,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(121)e\left(\frac{1}{21}\right) e(23)e\left(\frac{2}{3}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) e(821)e\left(\frac{8}{21}\right) e(23)e\left(\frac{2}{3}\right) e(821)e\left(\frac{8}{21}\right)
χ3528(3217,⋅)\chi_{3528}(3217,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(821)e\left(\frac{8}{21}\right) e(13)e\left(\frac{1}{3}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) e(121)e\left(\frac{1}{21}\right) e(13)e\left(\frac{1}{3}\right) e(121)e\left(\frac{1}{21}\right)
χ3528(3481,⋅)\chi_{3528}(3481,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(23)e\left(\frac{2}{3}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(23)e\left(\frac{2}{3}\right) e(1721)e\left(\frac{17}{21}\right)