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Properties

Label 1386.bx
Modulus 13861386
Conductor 7777
Order 1515
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1386, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([0,10,6])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(37,1386)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 13861386
Conductor: 7777
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1515
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 77.m
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(ζ15)\Q(\zeta_{15})
Fixed field: 15.15.886528337182930278529.1

Characters in Galois orbit

Character −1-1 11 55 1313 1717 1919 2323 2525 2929 3131 3737 4141
χ1386(37,⋅)\chi_{1386}(37,\cdot) 11 11 e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(23)e\left(\frac{2}{3}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right)
χ1386(163,⋅)\chi_{1386}(163,\cdot) 11 11 e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(23)e\left(\frac{2}{3}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right)
χ1386(235,⋅)\chi_{1386}(235,\cdot) 11 11 e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(13)e\left(\frac{1}{3}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right)
χ1386(289,⋅)\chi_{1386}(289,\cdot) 11 11 e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(23)e\left(\frac{2}{3}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right)
χ1386(361,⋅)\chi_{1386}(361,\cdot) 11 11 e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(13)e\left(\frac{1}{3}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right)
χ1386(487,⋅)\chi_{1386}(487,\cdot) 11 11 e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(13)e\left(\frac{1}{3}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right)
χ1386(1171,⋅)\chi_{1386}(1171,\cdot) 11 11 e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(23)e\left(\frac{2}{3}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right)
χ1386(1369,⋅)\chi_{1386}(1369,\cdot) 11 11 e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(13)e\left(\frac{1}{3}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right)