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Properties

Label 1925.eo
Modulus 19251925
Conductor 7777
Order 3030
Real no
Primitive no
Minimal yes
Parity odd

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1925, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,10,21]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(51,1925))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 19251925
Conductor: 7777
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3030
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 77.o
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ15)\Q(\zeta_{15})
Fixed field: 30.0.1046076147688308987260717152173116396995512371.1

Characters in Galois orbit

Character −1-1 11 22 33 44 66 88 99 1212 1313 1616 1717
χ1925(51,⋅)\chi_{1925}(51,\cdot) −1-1 11 e(1130)e\left(\frac{11}{30}\right) e(1415)e\left(\frac{14}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(310)e\left(\frac{3}{10}\right) e(110)e\left(\frac{1}{10}\right) e(1315)e\left(\frac{13}{15}\right) e(23)e\left(\frac{2}{3}\right) e(710)e\left(\frac{7}{10}\right) e(715)e\left(\frac{7}{15}\right) e(1930)e\left(\frac{19}{30}\right)
χ1925(151,⋅)\chi_{1925}(151,\cdot) −1-1 11 e(1930)e\left(\frac{19}{30}\right) e(115)e\left(\frac{1}{15}\right) e(415)e\left(\frac{4}{15}\right) e(710)e\left(\frac{7}{10}\right) e(910)e\left(\frac{9}{10}\right) e(215)e\left(\frac{2}{15}\right) e(13)e\left(\frac{1}{3}\right) e(310)e\left(\frac{3}{10}\right) e(815)e\left(\frac{8}{15}\right) e(1130)e\left(\frac{11}{30}\right)
χ1925(226,⋅)\chi_{1925}(226,\cdot) −1-1 11 e(1730)e\left(\frac{17}{30}\right) e(815)e\left(\frac{8}{15}\right) e(215)e\left(\frac{2}{15}\right) e(110)e\left(\frac{1}{10}\right) e(710)e\left(\frac{7}{10}\right) e(115)e\left(\frac{1}{15}\right) e(23)e\left(\frac{2}{3}\right) e(910)e\left(\frac{9}{10}\right) e(415)e\left(\frac{4}{15}\right) e(1330)e\left(\frac{13}{30}\right)
χ1925(326,⋅)\chi_{1925}(326,\cdot) −1-1 11 e(130)e\left(\frac{1}{30}\right) e(415)e\left(\frac{4}{15}\right) e(115)e\left(\frac{1}{15}\right) e(310)e\left(\frac{3}{10}\right) e(110)e\left(\frac{1}{10}\right) e(815)e\left(\frac{8}{15}\right) e(13)e\left(\frac{1}{3}\right) e(710)e\left(\frac{7}{10}\right) e(215)e\left(\frac{2}{15}\right) e(2930)e\left(\frac{29}{30}\right)
χ1925(501,⋅)\chi_{1925}(501,\cdot) −1-1 11 e(730)e\left(\frac{7}{30}\right) e(1315)e\left(\frac{13}{15}\right) e(715)e\left(\frac{7}{15}\right) e(110)e\left(\frac{1}{10}\right) e(710)e\left(\frac{7}{10}\right) e(1115)e\left(\frac{11}{15}\right) e(13)e\left(\frac{1}{3}\right) e(910)e\left(\frac{9}{10}\right) e(1415)e\left(\frac{14}{15}\right) e(2330)e\left(\frac{23}{30}\right)
χ1925(926,⋅)\chi_{1925}(926,\cdot) −1-1 11 e(2330)e\left(\frac{23}{30}\right) e(215)e\left(\frac{2}{15}\right) e(815)e\left(\frac{8}{15}\right) e(910)e\left(\frac{9}{10}\right) e(310)e\left(\frac{3}{10}\right) e(415)e\left(\frac{4}{15}\right) e(23)e\left(\frac{2}{3}\right) e(110)e\left(\frac{1}{10}\right) e(115)e\left(\frac{1}{15}\right) e(730)e\left(\frac{7}{30}\right)
χ1925(1201,⋅)\chi_{1925}(1201,\cdot) −1-1 11 e(1330)e\left(\frac{13}{30}\right) e(715)e\left(\frac{7}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(910)e\left(\frac{9}{10}\right) e(310)e\left(\frac{3}{10}\right) e(1415)e\left(\frac{14}{15}\right) e(13)e\left(\frac{1}{3}\right) e(110)e\left(\frac{1}{10}\right) e(1115)e\left(\frac{11}{15}\right) e(1730)e\left(\frac{17}{30}\right)
χ1925(1801,⋅)\chi_{1925}(1801,\cdot) −1-1 11 e(2930)e\left(\frac{29}{30}\right) e(1115)e\left(\frac{11}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(710)e\left(\frac{7}{10}\right) e(910)e\left(\frac{9}{10}\right) e(715)e\left(\frac{7}{15}\right) e(23)e\left(\frac{2}{3}\right) e(310)e\left(\frac{3}{10}\right) e(1315)e\left(\frac{13}{15}\right) e(130)e\left(\frac{1}{30}\right)