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Properties

Label 637.bi
Modulus 637637
Conductor 637637
Order 2121
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([20,14])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(16,637)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 637637
Conductor: 637637
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2121
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content 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 22 33 44 55 66 88 99 1010 1111 1212
χ637(16,⋅)\chi_{637}(16,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1721)e\left(\frac{17}{21}\right) e(1121)e\left(\frac{11}{21}\right) e(17)e\left(\frac{1}{7}\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(521)e\left(\frac{5}{21}\right)
χ637(74,⋅)\chi_{637}(74,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(121)e\left(\frac{1}{21}\right) e(17)e\left(\frac{1}{7}\right) e(121)e\left(\frac{1}{21}\right) e(1321)e\left(\frac{13}{21}\right) e(57)e\left(\frac{5}{7}\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(421)e\left(\frac{4}{21}\right)
χ637(107,⋅)\chi_{637}(107,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(821)e\left(\frac{8}{21}\right) e(17)e\left(\frac{1}{7}\right) e(821)e\left(\frac{8}{21}\right) e(2021)e\left(\frac{20}{21}\right) e(57)e\left(\frac{5}{7}\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(1121)e\left(\frac{11}{21}\right)
χ637(198,⋅)\chi_{637}(198,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(67)e\left(\frac{6}{7}\right) e(2021)e\left(\frac{20}{21}\right) e(821)e\left(\frac{8}{21}\right) e(27)e\left(\frac{2}{7}\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(1721)e\left(\frac{17}{21}\right)
χ637(256,⋅)\chi_{637}(256,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(67)e\left(\frac{6}{7}\right) e(1321)e\left(\frac{13}{21}\right) e(121)e\left(\frac{1}{21}\right) e(27)e\left(\frac{2}{7}\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(1021)e\left(\frac{10}{21}\right)
χ637(289,⋅)\chi_{637}(289,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(47)e\left(\frac{4}{7}\right) e(1121)e\left(\frac{11}{21}\right) e(1721)e\left(\frac{17}{21}\right) e(67)e\left(\frac{6}{7}\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(221)e\left(\frac{2}{21}\right)
χ637(347,⋅)\chi_{637}(347,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(57)e\left(\frac{5}{7}\right) e(1921)e\left(\frac{19}{21}\right) e(1621)e\left(\frac{16}{21}\right) e(47)e\left(\frac{4}{7}\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(1321)e\left(\frac{13}{21}\right)
χ637(380,⋅)\chi_{637}(380,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(221)e\left(\frac{2}{21}\right) e(27)e\left(\frac{2}{7}\right) e(221)e\left(\frac{2}{21}\right) e(521)e\left(\frac{5}{21}\right) e(37)e\left(\frac{3}{7}\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(821)e\left(\frac{8}{21}\right)
χ637(438,⋅)\chi_{637}(438,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(421)e\left(\frac{4}{21}\right) e(47)e\left(\frac{4}{7}\right) e(421)e\left(\frac{4}{21}\right) e(1021)e\left(\frac{10}{21}\right) e(67)e\left(\frac{6}{7}\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(1621)e\left(\frac{16}{21}\right)
χ637(529,⋅)\chi_{637}(529,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(37)e\left(\frac{3}{7}\right) e(1021)e\left(\frac{10}{21}\right) e(421)e\left(\frac{4}{21}\right) e(17)e\left(\frac{1}{7}\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(1921)e\left(\frac{19}{21}\right)
χ637(562,⋅)\chi_{637}(562,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(521)e\left(\frac{5}{21}\right) e(57)e\left(\frac{5}{7}\right) e(521)e\left(\frac{5}{21}\right) e(221)e\left(\frac{2}{21}\right) e(47)e\left(\frac{4}{7}\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(2021)e\left(\frac{20}{21}\right)
χ637(620,⋅)\chi_{637}(620,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(27)e\left(\frac{2}{7}\right) e(1621)e\left(\frac{16}{21}\right) e(1921)e\left(\frac{19}{21}\right) e(37)e\left(\frac{3}{7}\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(121)e\left(\frac{1}{21}\right)