Properties

Label 5400.dz
Modulus 54005400
Conductor 900900
Order 3030
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5400, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([15,0,25,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(71,5400)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 54005400
Conductor: 900900
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: no, induced from 900.br
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
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: Number field defined by a degree 30 polynomial

Characters in Galois orbit

Character 1-1 11 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ5400(71,)\chi_{5400}(71,\cdot) 11 11 e(56)e\left(\frac{5}{6}\right) e(1415)e\left(\frac{14}{15}\right) e(115)e\left(\frac{1}{15}\right) e(310)e\left(\frac{3}{10}\right) e(310)e\left(\frac{3}{10}\right) e(415)e\left(\frac{4}{15}\right) e(130)e\left(\frac{1}{30}\right) e(2930)e\left(\frac{29}{30}\right) e(25)e\left(\frac{2}{5}\right) e(1730)e\left(\frac{17}{30}\right)
χ5400(791,)\chi_{5400}(791,\cdot) 11 11 e(16)e\left(\frac{1}{6}\right) e(1315)e\left(\frac{13}{15}\right) e(215)e\left(\frac{2}{15}\right) e(110)e\left(\frac{1}{10}\right) e(110)e\left(\frac{1}{10}\right) e(815)e\left(\frac{8}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(1330)e\left(\frac{13}{30}\right) e(45)e\left(\frac{4}{5}\right) e(1930)e\left(\frac{19}{30}\right)
χ5400(1871,)\chi_{5400}(1871,\cdot) 11 11 e(16)e\left(\frac{1}{6}\right) e(415)e\left(\frac{4}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(310)e\left(\frac{3}{10}\right) e(310)e\left(\frac{3}{10}\right) e(1415)e\left(\frac{14}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(1930)e\left(\frac{19}{30}\right) e(25)e\left(\frac{2}{5}\right) e(730)e\left(\frac{7}{30}\right)
χ5400(2231,)\chi_{5400}(2231,\cdot) 11 11 e(56)e\left(\frac{5}{6}\right) e(1115)e\left(\frac{11}{15}\right) e(415)e\left(\frac{4}{15}\right) e(710)e\left(\frac{7}{10}\right) e(710)e\left(\frac{7}{10}\right) e(115)e\left(\frac{1}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(1130)e\left(\frac{11}{30}\right) e(35)e\left(\frac{3}{5}\right) e(2330)e\left(\frac{23}{30}\right)
χ5400(3311,)\chi_{5400}(3311,\cdot) 11 11 e(56)e\left(\frac{5}{6}\right) e(215)e\left(\frac{2}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(910)e\left(\frac{9}{10}\right) e(910)e\left(\frac{9}{10}\right) e(715)e\left(\frac{7}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(1730)e\left(\frac{17}{30}\right) e(15)e\left(\frac{1}{5}\right) e(1130)e\left(\frac{11}{30}\right)
χ5400(4031,)\chi_{5400}(4031,\cdot) 11 11 e(16)e\left(\frac{1}{6}\right) e(115)e\left(\frac{1}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(710)e\left(\frac{7}{10}\right) e(710)e\left(\frac{7}{10}\right) e(1115)e\left(\frac{11}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(130)e\left(\frac{1}{30}\right) e(35)e\left(\frac{3}{5}\right) e(1330)e\left(\frac{13}{30}\right)
χ5400(4391,)\chi_{5400}(4391,\cdot) 11 11 e(56)e\left(\frac{5}{6}\right) e(815)e\left(\frac{8}{15}\right) e(715)e\left(\frac{7}{15}\right) e(110)e\left(\frac{1}{10}\right) e(110)e\left(\frac{1}{10}\right) e(1315)e\left(\frac{13}{15}\right) e(730)e\left(\frac{7}{30}\right) e(2330)e\left(\frac{23}{30}\right) e(45)e\left(\frac{4}{5}\right) e(2930)e\left(\frac{29}{30}\right)
χ5400(5111,)\chi_{5400}(5111,\cdot) 11 11 e(16)e\left(\frac{1}{6}\right) e(715)e\left(\frac{7}{15}\right) e(815)e\left(\frac{8}{15}\right) e(910)e\left(\frac{9}{10}\right) e(910)e\left(\frac{9}{10}\right) e(215)e\left(\frac{2}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(730)e\left(\frac{7}{30}\right) e(15)e\left(\frac{1}{5}\right) e(130)e\left(\frac{1}{30}\right)