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Properties

Label 132300.kx
Modulus 132300132300
Conductor 63006300
Order 3030
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(132300, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([15,20,27,25]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,132300))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 132300132300
Conductor: 63006300
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3030
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 6300.hz
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
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 30 polynomial

Characters in Galois orbit

Character −1-1 11 1111 1313 1717 1919 2323 2929 3131 3737 4141 4343
χ132300(19,⋅)\chi_{132300}(19,\cdot) 11 11 e(910)e\left(\frac{9}{10}\right) 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(25)e\left(\frac{2}{5}\right) e(715)e\left(\frac{7}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(1330)e\left(\frac{13}{30}\right) e(23)e\left(\frac{2}{3}\right)
χ132300(15319,⋅)\chi_{132300}(15319,\cdot) 11 11 e(910)e\left(\frac{9}{10}\right) 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(25)e\left(\frac{2}{5}\right) e(215)e\left(\frac{2}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(2330)e\left(\frac{23}{30}\right) e(13)e\left(\frac{1}{3}\right)
χ132300(26479,⋅)\chi_{132300}(26479,\cdot) 11 11 e(110)e\left(\frac{1}{10}\right) 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(35)e\left(\frac{3}{5}\right) e(1315)e\left(\frac{13}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(730)e\left(\frac{7}{30}\right) e(23)e\left(\frac{2}{3}\right)
χ132300(41779,⋅)\chi_{132300}(41779,\cdot) 11 11 e(110)e\left(\frac{1}{10}\right) 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(35)e\left(\frac{3}{5}\right) e(815)e\left(\frac{8}{15}\right) e(215)e\left(\frac{2}{15}\right) e(730)e\left(\frac{7}{30}\right) e(1730)e\left(\frac{17}{30}\right) e(13)e\left(\frac{1}{3}\right)
χ132300(52939,⋅)\chi_{132300}(52939,\cdot) 11 11 e(310)e\left(\frac{3}{10}\right) 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(45)e\left(\frac{4}{5}\right) e(415)e\left(\frac{4}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(130)e\left(\frac{1}{30}\right) e(23)e\left(\frac{2}{3}\right)
χ132300(68239,⋅)\chi_{132300}(68239,\cdot) 11 11 e(310)e\left(\frac{3}{10}\right) 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(45)e\left(\frac{4}{5}\right) e(1415)e\left(\frac{14}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(130)e\left(\frac{1}{30}\right) e(1130)e\left(\frac{11}{30}\right) e(13)e\left(\frac{1}{3}\right)
χ132300(105859,⋅)\chi_{132300}(105859,\cdot) 11 11 e(710)e\left(\frac{7}{10}\right) 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(15)e\left(\frac{1}{5}\right) e(115)e\left(\frac{1}{15}\right) e(415)e\left(\frac{4}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(1930)e\left(\frac{19}{30}\right) e(23)e\left(\frac{2}{3}\right)
χ132300(121159,⋅)\chi_{132300}(121159,\cdot) 11 11 e(710)e\left(\frac{7}{10}\right) 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(15)e\left(\frac{1}{5}\right) e(1115)e\left(\frac{11}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(2930)e\left(\frac{29}{30}\right) e(13)e\left(\frac{1}{3}\right)