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Properties

Label 4675.he
Modulus 46754675
Conductor 46754675
Order 4040
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4675, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([32,16,15]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(236,4675))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 46754675
Conductor: 46754675
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4040
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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(ζ40)\Q(\zeta_{40})
Fixed field: Number field defined by a degree 40 polynomial

Characters in Galois orbit

Character −1-1 11 22 33 44 66 77 88 99 1212 1313 1414
χ4675(236,⋅)\chi_{4675}(236,\cdot) 11 11 e(920)e\left(\frac{9}{20}\right) e(740)e\left(\frac{7}{40}\right) e(910)e\left(\frac{9}{10}\right) e(58)e\left(\frac{5}{8}\right) e(3740)e\left(\frac{37}{40}\right) e(720)e\left(\frac{7}{20}\right) e(720)e\left(\frac{7}{20}\right) e(340)e\left(\frac{3}{40}\right) e(110)e\left(\frac{1}{10}\right) e(38)e\left(\frac{3}{8}\right)
χ4675(416,⋅)\chi_{4675}(416,\cdot) 11 11 e(1120)e\left(\frac{11}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(110)e\left(\frac{1}{10}\right) e(38)e\left(\frac{3}{8}\right) e(340)e\left(\frac{3}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(910)e\left(\frac{9}{10}\right) e(58)e\left(\frac{5}{8}\right)
χ4675(631,⋅)\chi_{4675}(631,\cdot) 11 11 e(1720)e\left(\frac{17}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(710)e\left(\frac{7}{10}\right) e(18)e\left(\frac{1}{8}\right) e(140)e\left(\frac{1}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(310)e\left(\frac{3}{10}\right) e(78)e\left(\frac{7}{8}\right)
χ4675(971,⋅)\chi_{4675}(971,\cdot) 11 11 e(1320)e\left(\frac{13}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(310)e\left(\frac{3}{10}\right) e(18)e\left(\frac{1}{8}\right) e(940)e\left(\frac{9}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(710)e\left(\frac{7}{10}\right) e(78)e\left(\frac{7}{8}\right)
χ4675(1181,⋅)\chi_{4675}(1181,\cdot) 11 11 e(720)e\left(\frac{7}{20}\right) e(140)e\left(\frac{1}{40}\right) e(710)e\left(\frac{7}{10}\right) e(38)e\left(\frac{3}{8}\right) e(1140)e\left(\frac{11}{40}\right) e(120)e\left(\frac{1}{20}\right) e(120)e\left(\frac{1}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(310)e\left(\frac{3}{10}\right) e(58)e\left(\frac{5}{8}\right)
χ4675(1521,⋅)\chi_{4675}(1521,\cdot) 11 11 e(320)e\left(\frac{3}{20}\right) e(940)e\left(\frac{9}{40}\right) e(310)e\left(\frac{3}{10}\right) e(38)e\left(\frac{3}{8}\right) e(1940)e\left(\frac{19}{40}\right) e(920)e\left(\frac{9}{20}\right) e(920)e\left(\frac{9}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(710)e\left(\frac{7}{10}\right) e(58)e\left(\frac{5}{8}\right)
χ4675(2066,⋅)\chi_{4675}(2066,\cdot) 11 11 e(1120)e\left(\frac{11}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(110)e\left(\frac{1}{10}\right) e(78)e\left(\frac{7}{8}\right) e(2340)e\left(\frac{23}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(910)e\left(\frac{9}{10}\right) e(18)e\left(\frac{1}{8}\right)
χ4675(2161,⋅)\chi_{4675}(2161,\cdot) 11 11 e(920)e\left(\frac{9}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(910)e\left(\frac{9}{10}\right) e(18)e\left(\frac{1}{8}\right) e(1740)e\left(\frac{17}{40}\right) e(720)e\left(\frac{7}{20}\right) e(720)e\left(\frac{7}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(110)e\left(\frac{1}{10}\right) e(78)e\left(\frac{7}{8}\right)
χ4675(2616,⋅)\chi_{4675}(2616,\cdot) 11 11 e(120)e\left(\frac{1}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(110)e\left(\frac{1}{10}\right) e(58)e\left(\frac{5}{8}\right) e(1340)e\left(\frac{13}{40}\right) e(320)e\left(\frac{3}{20}\right) e(320)e\left(\frac{3}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(910)e\left(\frac{9}{10}\right) e(38)e\left(\frac{3}{8}\right)
χ4675(2711,⋅)\chi_{4675}(2711,\cdot) 11 11 e(1920)e\left(\frac{19}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(910)e\left(\frac{9}{10}\right) e(38)e\left(\frac{3}{8}\right) e(2740)e\left(\frac{27}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(110)e\left(\frac{1}{10}\right) e(58)e\left(\frac{5}{8}\right)
χ4675(2831,⋅)\chi_{4675}(2831,\cdot) 11 11 e(720)e\left(\frac{7}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(710)e\left(\frac{7}{10}\right) e(78)e\left(\frac{7}{8}\right) e(3140)e\left(\frac{31}{40}\right) e(120)e\left(\frac{1}{20}\right) e(120)e\left(\frac{1}{20}\right) e(940)e\left(\frac{9}{40}\right) e(310)e\left(\frac{3}{10}\right) e(18)e\left(\frac{1}{8}\right)
χ4675(3171,⋅)\chi_{4675}(3171,\cdot) 11 11 e(320)e\left(\frac{3}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(310)e\left(\frac{3}{10}\right) e(78)e\left(\frac{7}{8}\right) e(3940)e\left(\frac{39}{40}\right) e(920)e\left(\frac{9}{20}\right) e(920)e\left(\frac{9}{20}\right) e(140)e\left(\frac{1}{40}\right) e(710)e\left(\frac{7}{10}\right) e(18)e\left(\frac{1}{8}\right)
χ4675(3381,⋅)\chi_{4675}(3381,\cdot) 11 11 e(1720)e\left(\frac{17}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(710)e\left(\frac{7}{10}\right) e(58)e\left(\frac{5}{8}\right) e(2140)e\left(\frac{21}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(310)e\left(\frac{3}{10}\right) e(38)e\left(\frac{3}{8}\right)
χ4675(3721,⋅)\chi_{4675}(3721,\cdot) 11 11 e(1320)e\left(\frac{13}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(310)e\left(\frac{3}{10}\right) e(58)e\left(\frac{5}{8}\right) e(2940)e\left(\frac{29}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(710)e\left(\frac{7}{10}\right) e(38)e\left(\frac{3}{8}\right)
χ4675(4361,⋅)\chi_{4675}(4361,\cdot) 11 11 e(1920)e\left(\frac{19}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(910)e\left(\frac{9}{10}\right) e(78)e\left(\frac{7}{8}\right) e(740)e\left(\frac{7}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(110)e\left(\frac{1}{10}\right) e(18)e\left(\frac{1}{8}\right)
χ4675(4541,⋅)\chi_{4675}(4541,\cdot) 11 11 e(120)e\left(\frac{1}{20}\right) e(340)e\left(\frac{3}{40}\right) e(110)e\left(\frac{1}{10}\right) e(18)e\left(\frac{1}{8}\right) e(3340)e\left(\frac{33}{40}\right) e(320)e\left(\frac{3}{20}\right) e(320)e\left(\frac{3}{20}\right) e(740)e\left(\frac{7}{40}\right) e(910)e\left(\frac{9}{10}\right) e(78)e\left(\frac{7}{8}\right)