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Properties

Label 7448.fr
Modulus 74487448
Conductor 4949
Order 2121
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7448, base_ring=CyclotomicField(42))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,40,0]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(305,7448))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 74487448
Conductor: 4949
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2121
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 49.g
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 33 55 99 1111 1313 1515 1717 2323 2525 2727
χ7448(305,⋅)\chi_{7448}(305,\cdot) 11 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(221)e\left(\frac{2}{21}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(421)e\left(\frac{4}{21}\right) e(521)e\left(\frac{5}{21}\right) e(67)e\left(\frac{6}{7}\right)
χ7448(457,⋅)\chi_{7448}(457,\cdot) 11 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(121)e\left(\frac{1}{21}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(221)e\left(\frac{2}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(37)e\left(\frac{3}{7}\right)
χ7448(1369,⋅)\chi_{7448}(1369,\cdot) 11 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(2021)e\left(\frac{20}{21}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(221)e\left(\frac{2}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(821)e\left(\frac{8}{21}\right) e(47)e\left(\frac{4}{7}\right)
χ7448(1521,⋅)\chi_{7448}(1521,\cdot) 11 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(1621)e\left(\frac{16}{21}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(67)e\left(\frac{6}{7}\right)
χ7448(2433,⋅)\chi_{7448}(2433,\cdot) 11 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(1721)e\left(\frac{17}{21}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(821)e\left(\frac{8}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(27)e\left(\frac{2}{7}\right)
χ7448(2585,⋅)\chi_{7448}(2585,\cdot) 11 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(1021)e\left(\frac{10}{21}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(121)e\left(\frac{1}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(421)e\left(\frac{4}{21}\right) e(27)e\left(\frac{2}{7}\right)
χ7448(3649,⋅)\chi_{7448}(3649,\cdot) 11 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(421)e\left(\frac{4}{21}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(821)e\left(\frac{8}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(57)e\left(\frac{5}{7}\right)
χ7448(4561,⋅)\chi_{7448}(4561,\cdot) 11 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(1121)e\left(\frac{11}{21}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(121)e\left(\frac{1}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(57)e\left(\frac{5}{7}\right)
χ7448(4713,⋅)\chi_{7448}(4713,\cdot) 11 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(1921)e\left(\frac{19}{21}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(421)e\left(\frac{4}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(17)e\left(\frac{1}{7}\right)
χ7448(5625,⋅)\chi_{7448}(5625,\cdot) 11 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(821)e\left(\frac{8}{21}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(521)e\left(\frac{5}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(37)e\left(\frac{3}{7}\right)
χ7448(5777,⋅)\chi_{7448}(5777,\cdot) 11 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(1321)e\left(\frac{13}{21}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(521)e\left(\frac{5}{21}\right) e(121)e\left(\frac{1}{21}\right) e(47)e\left(\frac{4}{7}\right)
χ7448(6689,⋅)\chi_{7448}(6689,\cdot) 11 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(521)e\left(\frac{5}{21}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(221)e\left(\frac{2}{21}\right) e(17)e\left(\frac{1}{7}\right)