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Properties

Label 725.bd
Modulus 725725
Conductor 145145
Order 2828
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(725, base_ring=CyclotomicField(28))
 
M = H._module
 
chi = DirichletCharacter(H, M([21,13]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(43,725))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 725725
Conductor: 145145
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2828
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 145.t
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(ζ28)\Q(\zeta_{28})
Fixed field: 28.28.1455848000512373226044338588471370773272037506103515625.2

Characters in Galois orbit

Character −1-1 11 22 33 44 66 77 88 99 1111 1212 1313
χ725(43,⋅)\chi_{725}(43,\cdot) 11 11 e(314)e\left(\frac{3}{14}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(928)e\left(\frac{9}{28}\right) e(914)e\left(\frac{9}{14}\right) e(17)e\left(\frac{1}{7}\right) e(1728)e\left(\frac{17}{28}\right) 11 e(1728)e\left(\frac{17}{28}\right)
χ725(118,⋅)\chi_{725}(118,\cdot) 11 11 e(1114)e\left(\frac{11}{14}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(314)e\left(\frac{3}{14}\right) e(528)e\left(\frac{5}{28}\right) e(514)e\left(\frac{5}{14}\right) e(67)e\left(\frac{6}{7}\right) e(2528)e\left(\frac{25}{28}\right) 11 e(2528)e\left(\frac{25}{28}\right)
χ725(182,⋅)\chi_{725}(182,\cdot) 11 11 e(514)e\left(\frac{5}{14}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(914)e\left(\frac{9}{14}\right) e(1528)e\left(\frac{15}{28}\right) e(114)e\left(\frac{1}{14}\right) e(47)e\left(\frac{4}{7}\right) e(1928)e\left(\frac{19}{28}\right) 11 e(1928)e\left(\frac{19}{28}\right)
χ725(193,⋅)\chi_{725}(193,\cdot) 11 11 e(114)e\left(\frac{1}{14}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(1728)e\left(\frac{17}{28}\right) e(314)e\left(\frac{3}{14}\right) e(57)e\left(\frac{5}{7}\right) e(128)e\left(\frac{1}{28}\right) 11 e(128)e\left(\frac{1}{28}\right)
χ725(243,⋅)\chi_{725}(243,\cdot) 11 11 e(914)e\left(\frac{9}{14}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(514)e\left(\frac{5}{14}\right) e(1328)e\left(\frac{13}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(37)e\left(\frac{3}{7}\right) e(928)e\left(\frac{9}{28}\right) 11 e(928)e\left(\frac{9}{28}\right)
χ725(293,⋅)\chi_{725}(293,\cdot) 11 11 e(1314)e\left(\frac{13}{14}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(114)e\left(\frac{1}{14}\right) e(2528)e\left(\frac{25}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(27)e\left(\frac{2}{7}\right) e(1328)e\left(\frac{13}{28}\right) 11 e(1328)e\left(\frac{13}{28}\right)
χ725(432,⋅)\chi_{725}(432,\cdot) 11 11 e(1314)e\left(\frac{13}{14}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(114)e\left(\frac{1}{14}\right) e(1128)e\left(\frac{11}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(27)e\left(\frac{2}{7}\right) e(2728)e\left(\frac{27}{28}\right) 11 e(2728)e\left(\frac{27}{28}\right)
χ725(482,⋅)\chi_{725}(482,\cdot) 11 11 e(914)e\left(\frac{9}{14}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(514)e\left(\frac{5}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(37)e\left(\frac{3}{7}\right) e(2328)e\left(\frac{23}{28}\right) 11 e(2328)e\left(\frac{23}{28}\right)
χ725(532,⋅)\chi_{725}(532,\cdot) 11 11 e(114)e\left(\frac{1}{14}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(328)e\left(\frac{3}{28}\right) e(314)e\left(\frac{3}{14}\right) e(57)e\left(\frac{5}{7}\right) e(1528)e\left(\frac{15}{28}\right) 11 e(1528)e\left(\frac{15}{28}\right)
χ725(543,⋅)\chi_{725}(543,\cdot) 11 11 e(514)e\left(\frac{5}{14}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(914)e\left(\frac{9}{14}\right) e(128)e\left(\frac{1}{28}\right) e(114)e\left(\frac{1}{14}\right) e(47)e\left(\frac{4}{7}\right) e(528)e\left(\frac{5}{28}\right) 11 e(528)e\left(\frac{5}{28}\right)
χ725(607,⋅)\chi_{725}(607,\cdot) 11 11 e(1114)e\left(\frac{11}{14}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(314)e\left(\frac{3}{14}\right) e(1928)e\left(\frac{19}{28}\right) e(514)e\left(\frac{5}{14}\right) e(67)e\left(\frac{6}{7}\right) e(1128)e\left(\frac{11}{28}\right) 11 e(1128)e\left(\frac{11}{28}\right)
χ725(682,⋅)\chi_{725}(682,\cdot) 11 11 e(314)e\left(\frac{3}{14}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(2328)e\left(\frac{23}{28}\right) e(914)e\left(\frac{9}{14}\right) e(17)e\left(\frac{1}{7}\right) e(328)e\left(\frac{3}{28}\right) 11 e(328)e\left(\frac{3}{28}\right)