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Properties

Label 475.z
Modulus 475475
Conductor 475475
Order 3030
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([27,25])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(69,475)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 475475
Conductor: 475475
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 3030
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: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ15)\Q(\zeta_{15})
Fixed field: 30.0.41334267425810406820389890772071250779617912485264241695404052734375.1

Characters in Galois orbit

Character −1-1 11 22 33 44 66 77 88 99 1111 1212 1313
χ475(69,⋅)\chi_{475}(69,\cdot) −1-1 11 e(1115)e\left(\frac{11}{15}\right) e(215)e\left(\frac{2}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1315)e\left(\frac{13}{15}\right) −1-1 e(15)e\left(\frac{1}{5}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(415)e\left(\frac{4}{15}\right)
χ475(84,⋅)\chi_{475}(84,\cdot) −1-1 11 e(1315)e\left(\frac{13}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(1415)e\left(\frac{14}{15}\right) −1-1 e(35)e\left(\frac{3}{5}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(215)e\left(\frac{2}{15}\right)
χ475(164,⋅)\chi_{475}(164,\cdot) −1-1 11 e(215)e\left(\frac{2}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(415)e\left(\frac{4}{15}\right) e(115)e\left(\frac{1}{15}\right) −1-1 e(25)e\left(\frac{2}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(1315)e\left(\frac{13}{15}\right)
χ475(179,⋅)\chi_{475}(179,\cdot) −1-1 11 e(415)e\left(\frac{4}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(815)e\left(\frac{8}{15}\right) e(215)e\left(\frac{2}{15}\right) −1-1 e(45)e\left(\frac{4}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(1115)e\left(\frac{11}{15}\right)
χ475(259,⋅)\chi_{475}(259,\cdot) −1-1 11 e(815)e\left(\frac{8}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(115)e\left(\frac{1}{15}\right) e(415)e\left(\frac{4}{15}\right) −1-1 e(35)e\left(\frac{3}{5}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) e(715)e\left(\frac{7}{15}\right)
χ475(354,⋅)\chi_{475}(354,\cdot) −1-1 11 e(1415)e\left(\frac{14}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(715)e\left(\frac{7}{15}\right) −1-1 e(45)e\left(\frac{4}{5}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) e(115)e\left(\frac{1}{15}\right)
χ475(369,⋅)\chi_{475}(369,\cdot) −1-1 11 e(115)e\left(\frac{1}{15}\right) e(715)e\left(\frac{7}{15}\right) e(215)e\left(\frac{2}{15}\right) e(815)e\left(\frac{8}{15}\right) −1-1 e(15)e\left(\frac{1}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) e(1415)e\left(\frac{14}{15}\right)
χ475(464,⋅)\chi_{475}(464,\cdot) −1-1 11 e(715)e\left(\frac{7}{15}\right) e(415)e\left(\frac{4}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1115)e\left(\frac{11}{15}\right) −1-1 e(25)e\left(\frac{2}{5}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) e(815)e\left(\frac{8}{15}\right)