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Properties

Label 2320.ds
Modulus 23202320
Conductor 23202320
Order 2828
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2320, base_ring=CyclotomicField(28))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,21,21,18]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(13,2320))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 23202320
Conductor: 23202320
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2828
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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(ζ28)\Q(\zeta_{28})
Fixed field: Number field defined by a degree 28 polynomial

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1717 1919 2121 2323 2727
χ2320(13,⋅)\chi_{2320}(13,\cdot) −1-1 11 e(57)e\left(\frac{5}{7}\right) e(2728)e\left(\frac{27}{28}\right) e(37)e\left(\frac{3}{7}\right) e(2328)e\left(\frac{23}{28}\right) e(114)e\left(\frac{1}{14}\right) ii e(1528)e\left(\frac{15}{28}\right) e(1928)e\left(\frac{19}{28}\right) e(1728)e\left(\frac{17}{28}\right) e(17)e\left(\frac{1}{7}\right)
χ2320(93,⋅)\chi_{2320}(93,\cdot) −1-1 11 e(47)e\left(\frac{4}{7}\right) e(2328)e\left(\frac{23}{28}\right) e(17)e\left(\frac{1}{7}\right) e(328)e\left(\frac{3}{28}\right) e(514)e\left(\frac{5}{14}\right) ii e(1928)e\left(\frac{19}{28}\right) e(1128)e\left(\frac{11}{28}\right) e(128)e\left(\frac{1}{28}\right) e(57)e\left(\frac{5}{7}\right)
χ2320(357,⋅)\chi_{2320}(357,\cdot) −1-1 11 e(27)e\left(\frac{2}{7}\right) e(128)e\left(\frac{1}{28}\right) e(47)e\left(\frac{4}{7}\right) e(528)e\left(\frac{5}{28}\right) e(1314)e\left(\frac{13}{14}\right) −i-i e(1328)e\left(\frac{13}{28}\right) e(928)e\left(\frac{9}{28}\right) e(1128)e\left(\frac{11}{28}\right) e(67)e\left(\frac{6}{7}\right)
χ2320(573,⋅)\chi_{2320}(573,\cdot) −1-1 11 e(17)e\left(\frac{1}{7}\right) e(1128)e\left(\frac{11}{28}\right) e(27)e\left(\frac{2}{7}\right) e(2728)e\left(\frac{27}{28}\right) e(314)e\left(\frac{3}{14}\right) ii e(328)e\left(\frac{3}{28}\right) e(1528)e\left(\frac{15}{28}\right) e(928)e\left(\frac{9}{28}\right) e(37)e\left(\frac{3}{7}\right)
χ2320(1053,⋅)\chi_{2320}(1053,\cdot) −1-1 11 e(27)e\left(\frac{2}{7}\right) e(1528)e\left(\frac{15}{28}\right) e(47)e\left(\frac{4}{7}\right) e(1928)e\left(\frac{19}{28}\right) e(1314)e\left(\frac{13}{14}\right) ii e(2728)e\left(\frac{27}{28}\right) e(2328)e\left(\frac{23}{28}\right) e(2528)e\left(\frac{25}{28}\right) e(67)e\left(\frac{6}{7}\right)
χ2320(1077,⋅)\chi_{2320}(1077,\cdot) −1-1 11 e(67)e\left(\frac{6}{7}\right) e(1728)e\left(\frac{17}{28}\right) e(57)e\left(\frac{5}{7}\right) e(128)e\left(\frac{1}{28}\right) e(1114)e\left(\frac{11}{14}\right) −i-i e(2528)e\left(\frac{25}{28}\right) e(1328)e\left(\frac{13}{28}\right) e(1928)e\left(\frac{19}{28}\right) e(47)e\left(\frac{4}{7}\right)
χ2320(1397,⋅)\chi_{2320}(1397,\cdot) −1-1 11 e(37)e\left(\frac{3}{7}\right) e(528)e\left(\frac{5}{28}\right) e(67)e\left(\frac{6}{7}\right) e(2528)e\left(\frac{25}{28}\right) e(914)e\left(\frac{9}{14}\right) −i-i e(928)e\left(\frac{9}{28}\right) e(1728)e\left(\frac{17}{28}\right) e(2728)e\left(\frac{27}{28}\right) e(27)e\left(\frac{2}{7}\right)
χ2320(1637,⋅)\chi_{2320}(1637,\cdot) −1-1 11 e(57)e\left(\frac{5}{7}\right) e(1328)e\left(\frac{13}{28}\right) e(37)e\left(\frac{3}{7}\right) e(928)e\left(\frac{9}{28}\right) e(114)e\left(\frac{1}{14}\right) −i-i e(128)e\left(\frac{1}{28}\right) e(528)e\left(\frac{5}{28}\right) e(328)e\left(\frac{3}{28}\right) e(17)e\left(\frac{1}{7}\right)
χ2320(1717,⋅)\chi_{2320}(1717,\cdot) −1-1 11 e(47)e\left(\frac{4}{7}\right) e(928)e\left(\frac{9}{28}\right) e(17)e\left(\frac{1}{7}\right) e(1728)e\left(\frac{17}{28}\right) e(514)e\left(\frac{5}{14}\right) −i-i e(528)e\left(\frac{5}{28}\right) e(2528)e\left(\frac{25}{28}\right) e(1528)e\left(\frac{15}{28}\right) e(57)e\left(\frac{5}{7}\right)
χ2320(1773,⋅)\chi_{2320}(1773,\cdot) −1-1 11 e(67)e\left(\frac{6}{7}\right) e(328)e\left(\frac{3}{28}\right) e(57)e\left(\frac{5}{7}\right) e(1528)e\left(\frac{15}{28}\right) e(1114)e\left(\frac{11}{14}\right) ii e(1128)e\left(\frac{11}{28}\right) e(2728)e\left(\frac{27}{28}\right) e(528)e\left(\frac{5}{28}\right) e(47)e\left(\frac{4}{7}\right)
χ2320(2093,⋅)\chi_{2320}(2093,\cdot) −1-1 11 e(37)e\left(\frac{3}{7}\right) e(1928)e\left(\frac{19}{28}\right) e(67)e\left(\frac{6}{7}\right) e(1128)e\left(\frac{11}{28}\right) e(914)e\left(\frac{9}{14}\right) ii e(2328)e\left(\frac{23}{28}\right) e(328)e\left(\frac{3}{28}\right) e(1328)e\left(\frac{13}{28}\right) e(27)e\left(\frac{2}{7}\right)
χ2320(2197,⋅)\chi_{2320}(2197,\cdot) −1-1 11 e(17)e\left(\frac{1}{7}\right) e(2528)e\left(\frac{25}{28}\right) e(27)e\left(\frac{2}{7}\right) e(1328)e\left(\frac{13}{28}\right) e(314)e\left(\frac{3}{14}\right) −i-i e(1728)e\left(\frac{17}{28}\right) e(128)e\left(\frac{1}{28}\right) e(2328)e\left(\frac{23}{28}\right) e(37)e\left(\frac{3}{7}\right)