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Properties

Label 1575.cs
Modulus 15751575
Conductor 175175
Order 1515
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1575, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,18,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(46,1575))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 15751575
Conductor: 175175
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1515
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 175.q
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ15)\Q(\zeta_{15})
Fixed field: Number field defined by a degree 15 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 88 1111 1313 1616 1717 1919 2222 2323
χ1575(46,⋅)\chi_{1575}(46,\cdot) 11 11 e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\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)
χ1575(361,⋅)\chi_{1575}(361,\cdot) 11 11 e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\right) e(25)e\left(\frac{2}{5}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\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)
χ1575(541,⋅)\chi_{1575}(541,\cdot) 11 11 e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\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)
χ1575(856,⋅)\chi_{1575}(856,\cdot) 11 11 e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(35)e\left(\frac{3}{5}\right) e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\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)
χ1575(991,⋅)\chi_{1575}(991,\cdot) 11 11 e(815)e\left(\frac{8}{15}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(45)e\left(\frac{4}{5}\right) e(215)e\left(\frac{2}{15}\right) e(415)e\left(\frac{4}{15}\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)
χ1575(1171,⋅)\chi_{1575}(1171,\cdot) 11 11 e(415)e\left(\frac{4}{15}\right) e(815)e\left(\frac{8}{15}\right) e(45)e\left(\frac{4}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) e(115)e\left(\frac{1}{15}\right) e(215)e\left(\frac{2}{15}\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)
χ1575(1306,⋅)\chi_{1575}(1306,\cdot) 11 11 e(1115)e\left(\frac{11}{15}\right) e(715)e\left(\frac{7}{15}\right) e(15)e\left(\frac{1}{5}\right) e(115)e\left(\frac{1}{15}\right) e(35)e\left(\frac{3}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(1315)e\left(\frac{13}{15}\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)
χ1575(1486,⋅)\chi_{1575}(1486,\cdot) 11 11 e(715)e\left(\frac{7}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(25)e\left(\frac{2}{5}\right) e(215)e\left(\frac{2}{15}\right) e(15)e\left(\frac{1}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(1115)e\left(\frac{11}{15}\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)