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Properties

Label 1305.cd
Modulus 13051305
Conductor 145145
Order 2828
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([0,21,22])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(208,1305)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 13051305
Conductor: 145145
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2828
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 145.q
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ28)\Q(\zeta_{28})
Fixed field: 28.0.50201655190081835380839261671426578388690948486328125.1

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ1305(208,⋅)\chi_{1305}(208,\cdot) −1-1 11 e(1528)e\left(\frac{15}{28}\right) e(114)e\left(\frac{1}{14}\right) e(528)e\left(\frac{5}{28}\right) e(1728)e\left(\frac{17}{28}\right) e(914)e\left(\frac{9}{14}\right) e(1128)e\left(\frac{11}{28}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) ii e(47)e\left(\frac{4}{7}\right)
χ1305(352,⋅)\chi_{1305}(352,\cdot) −1-1 11 e(928)e\left(\frac{9}{28}\right) e(914)e\left(\frac{9}{14}\right) e(328)e\left(\frac{3}{28}\right) e(2728)e\left(\frac{27}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(128)e\left(\frac{1}{28}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) −i-i e(17)e\left(\frac{1}{7}\right)
χ1305(613,⋅)\chi_{1305}(613,\cdot) −1-1 11 e(2328)e\left(\frac{23}{28}\right) e(914)e\left(\frac{9}{14}\right) e(1728)e\left(\frac{17}{28}\right) e(1328)e\left(\frac{13}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(1528)e\left(\frac{15}{28}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) ii e(17)e\left(\frac{1}{7}\right)
χ1305(622,⋅)\chi_{1305}(622,\cdot) −1-1 11 e(2528)e\left(\frac{25}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(1928)e\left(\frac{19}{28}\right) e(114)e\left(\frac{1}{14}\right) e(928)e\left(\frac{9}{28}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) −i-i e(27)e\left(\frac{2}{7}\right)
χ1305(847,⋅)\chi_{1305}(847,\cdot) −1-1 11 e(1328)e\left(\frac{13}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(2328)e\left(\frac{23}{28}\right) e(1128)e\left(\frac{11}{28}\right) e(514)e\left(\frac{5}{14}\right) e(1728)e\left(\frac{17}{28}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) −i-i e(37)e\left(\frac{3}{7}\right)
χ1305(883,⋅)\chi_{1305}(883,\cdot) −1-1 11 e(1128)e\left(\frac{11}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(1328)e\left(\frac{13}{28}\right) e(528)e\left(\frac{5}{28}\right) e(114)e\left(\frac{1}{14}\right) e(2328)e\left(\frac{23}{28}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) ii e(27)e\left(\frac{2}{7}\right)
χ1305(892,⋅)\chi_{1305}(892,\cdot) −1-1 11 e(528)e\left(\frac{5}{28}\right) e(514)e\left(\frac{5}{14}\right) e(1128)e\left(\frac{11}{28}\right) e(1528)e\left(\frac{15}{28}\right) e(314)e\left(\frac{3}{14}\right) e(1328)e\left(\frac{13}{28}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) −i-i e(67)e\left(\frac{6}{7}\right)
χ1305(937,⋅)\chi_{1305}(937,\cdot) −1-1 11 e(1728)e\left(\frac{17}{28}\right) e(314)e\left(\frac{3}{14}\right) e(1528)e\left(\frac{15}{28}\right) e(2328)e\left(\frac{23}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(528)e\left(\frac{5}{28}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) −i-i e(57)e\left(\frac{5}{7}\right)
χ1305(1108,⋅)\chi_{1305}(1108,\cdot) −1-1 11 e(2728)e\left(\frac{27}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(928)e\left(\frac{9}{28}\right) e(2528)e\left(\frac{25}{28}\right) e(514)e\left(\frac{5}{14}\right) e(328)e\left(\frac{3}{28}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) ii e(37)e\left(\frac{3}{7}\right)
χ1305(1153,⋅)\chi_{1305}(1153,\cdot) −1-1 11 e(1928)e\left(\frac{19}{28}\right) e(514)e\left(\frac{5}{14}\right) e(2528)e\left(\frac{25}{28}\right) e(128)e\left(\frac{1}{28}\right) e(314)e\left(\frac{3}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) ii e(67)e\left(\frac{6}{7}\right)
χ1305(1198,⋅)\chi_{1305}(1198,\cdot) −1-1 11 e(328)e\left(\frac{3}{28}\right) e(314)e\left(\frac{3}{14}\right) e(128)e\left(\frac{1}{28}\right) e(928)e\left(\frac{9}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(1928)e\left(\frac{19}{28}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) ii e(57)e\left(\frac{5}{7}\right)
χ1305(1252,⋅)\chi_{1305}(1252,\cdot) −1-1 11 e(128)e\left(\frac{1}{28}\right) e(114)e\left(\frac{1}{14}\right) e(1928)e\left(\frac{19}{28}\right) e(328)e\left(\frac{3}{28}\right) e(914)e\left(\frac{9}{14}\right) e(2528)e\left(\frac{25}{28}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) −i-i e(47)e\left(\frac{4}{7}\right)