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Properties

Label 3072.t
Modulus 30723072
Conductor 6464
Order 1616
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3072, base_ring=CyclotomicField(16)) M = H._module chi = DirichletCharacter(H, M([8,5,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(319,3072)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 30723072
Conductor: 6464
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1616
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 64.j
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ16)\Q(\zeta_{16})
Fixed field: 16.0.604462909807314587353088.1

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ3072(319,⋅)\chi_{3072}(319,\cdot) −1-1 11 e(516)e\left(\frac{5}{16}\right) e(58)e\left(\frac{5}{8}\right) e(116)e\left(\frac{1}{16}\right) e(1116)e\left(\frac{11}{16}\right) −i-i e(1116)e\left(\frac{11}{16}\right) e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) e(716)e\left(\frac{7}{16}\right) 11
χ3072(703,⋅)\chi_{3072}(703,\cdot) −1-1 11 e(1116)e\left(\frac{11}{16}\right) e(38)e\left(\frac{3}{8}\right) e(1516)e\left(\frac{15}{16}\right) e(516)e\left(\frac{5}{16}\right) ii e(516)e\left(\frac{5}{16}\right) e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) e(916)e\left(\frac{9}{16}\right) 11
χ3072(1087,⋅)\chi_{3072}(1087,\cdot) −1-1 11 e(116)e\left(\frac{1}{16}\right) e(18)e\left(\frac{1}{8}\right) e(1316)e\left(\frac{13}{16}\right) e(1516)e\left(\frac{15}{16}\right) −i-i e(1516)e\left(\frac{15}{16}\right) e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1116)e\left(\frac{11}{16}\right) 11
χ3072(1471,⋅)\chi_{3072}(1471,\cdot) −1-1 11 e(716)e\left(\frac{7}{16}\right) e(78)e\left(\frac{7}{8}\right) e(1116)e\left(\frac{11}{16}\right) e(916)e\left(\frac{9}{16}\right) ii e(916)e\left(\frac{9}{16}\right) e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) e(1316)e\left(\frac{13}{16}\right) 11
χ3072(1855,⋅)\chi_{3072}(1855,\cdot) −1-1 11 e(1316)e\left(\frac{13}{16}\right) e(58)e\left(\frac{5}{8}\right) e(916)e\left(\frac{9}{16}\right) e(316)e\left(\frac{3}{16}\right) −i-i e(316)e\left(\frac{3}{16}\right) e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) e(1516)e\left(\frac{15}{16}\right) 11
χ3072(2239,⋅)\chi_{3072}(2239,\cdot) −1-1 11 e(316)e\left(\frac{3}{16}\right) e(38)e\left(\frac{3}{8}\right) e(716)e\left(\frac{7}{16}\right) e(1316)e\left(\frac{13}{16}\right) ii e(1316)e\left(\frac{13}{16}\right) e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) e(116)e\left(\frac{1}{16}\right) 11
χ3072(2623,⋅)\chi_{3072}(2623,\cdot) −1-1 11 e(916)e\left(\frac{9}{16}\right) e(18)e\left(\frac{1}{8}\right) e(516)e\left(\frac{5}{16}\right) e(716)e\left(\frac{7}{16}\right) −i-i e(716)e\left(\frac{7}{16}\right) e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) e(316)e\left(\frac{3}{16}\right) 11
χ3072(3007,⋅)\chi_{3072}(3007,\cdot) −1-1 11 e(1516)e\left(\frac{15}{16}\right) e(78)e\left(\frac{7}{8}\right) e(316)e\left(\frac{3}{16}\right) e(116)e\left(\frac{1}{16}\right) ii e(116)e\left(\frac{1}{16}\right) e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) e(516)e\left(\frac{5}{16}\right) 11