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Properties

Label 1734.k
Modulus 17341734
Conductor 289289
Order 1717
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1734, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([0,8])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(103,1734)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 17341734
Conductor: 289289
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1717
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 289.f
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ17)\Q(\zeta_{17})
Fixed field: Number field defined by a degree 17 polynomial

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1919 2323 2525 2929 3131 3535
χ1734(103,⋅)\chi_{1734}(103,\cdot) 11 11 e(1517)e\left(\frac{15}{17}\right) e(817)e\left(\frac{8}{17}\right) e(717)e\left(\frac{7}{17}\right) e(217)e\left(\frac{2}{17}\right) e(517)e\left(\frac{5}{17}\right) e(817)e\left(\frac{8}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(717)e\left(\frac{7}{17}\right) e(217)e\left(\frac{2}{17}\right) e(617)e\left(\frac{6}{17}\right)
χ1734(205,⋅)\chi_{1734}(205,\cdot) 11 11 e(1317)e\left(\frac{13}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(417)e\left(\frac{4}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(917)e\left(\frac{9}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(417)e\left(\frac{4}{17}\right) e(1217)e\left(\frac{12}{17}\right)
χ1734(307,⋅)\chi_{1734}(307,\cdot) 11 11 e(1117)e\left(\frac{11}{17}\right) e(717)e\left(\frac{7}{17}\right) e(417)e\left(\frac{4}{17}\right) e(617)e\left(\frac{6}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(717)e\left(\frac{7}{17}\right) e(517)e\left(\frac{5}{17}\right) e(417)e\left(\frac{4}{17}\right) e(617)e\left(\frac{6}{17}\right) e(117)e\left(\frac{1}{17}\right)
χ1734(409,⋅)\chi_{1734}(409,\cdot) 11 11 e(917)e\left(\frac{9}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(817)e\left(\frac{8}{17}\right) e(317)e\left(\frac{3}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(117)e\left(\frac{1}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(817)e\left(\frac{8}{17}\right) e(717)e\left(\frac{7}{17}\right)
χ1734(511,⋅)\chi_{1734}(511,\cdot) 11 11 e(717)e\left(\frac{7}{17}\right) e(617)e\left(\frac{6}{17}\right) e(117)e\left(\frac{1}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(817)e\left(\frac{8}{17}\right) e(617)e\left(\frac{6}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(117)e\left(\frac{1}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1317)e\left(\frac{13}{17}\right)
χ1734(613,⋅)\chi_{1734}(613,\cdot) 11 11 e(517)e\left(\frac{5}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(817)e\left(\frac{8}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(817)e\left(\frac{8}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(217)e\left(\frac{2}{17}\right)
χ1734(715,⋅)\chi_{1734}(715,\cdot) 11 11 e(317)e\left(\frac{3}{17}\right) e(517)e\left(\frac{5}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(117)e\left(\frac{1}{17}\right) e(517)e\left(\frac{5}{17}\right) e(617)e\left(\frac{6}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(817)e\left(\frac{8}{17}\right)
χ1734(817,⋅)\chi_{1734}(817,\cdot) 11 11 e(117)e\left(\frac{1}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(517)e\left(\frac{5}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(617)e\left(\frac{6}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(217)e\left(\frac{2}{17}\right) e(517)e\left(\frac{5}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(1417)e\left(\frac{14}{17}\right)
χ1734(919,⋅)\chi_{1734}(919,\cdot) 11 11 e(1617)e\left(\frac{16}{17}\right) e(417)e\left(\frac{4}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(117)e\left(\frac{1}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(417)e\left(\frac{4}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(117)e\left(\frac{1}{17}\right) e(317)e\left(\frac{3}{17}\right)
χ1734(1021,⋅)\chi_{1734}(1021,\cdot) 11 11 e(1417)e\left(\frac{14}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(217)e\left(\frac{2}{17}\right) e(317)e\left(\frac{3}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(217)e\left(\frac{2}{17}\right) e(317)e\left(\frac{3}{17}\right) e(917)e\left(\frac{9}{17}\right)
χ1734(1123,⋅)\chi_{1734}(1123,\cdot) 11 11 e(1217)e\left(\frac{12}{17}\right) e(317)e\left(\frac{3}{17}\right) e(917)e\left(\frac{9}{17}\right) e(517)e\left(\frac{5}{17}\right) e(417)e\left(\frac{4}{17}\right) e(317)e\left(\frac{3}{17}\right) e(717)e\left(\frac{7}{17}\right) e(917)e\left(\frac{9}{17}\right) e(517)e\left(\frac{5}{17}\right) e(1517)e\left(\frac{15}{17}\right)
χ1734(1225,⋅)\chi_{1734}(1225,\cdot) 11 11 e(1017)e\left(\frac{10}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(717)e\left(\frac{7}{17}\right) e(917)e\left(\frac{9}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(317)e\left(\frac{3}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(717)e\left(\frac{7}{17}\right) e(417)e\left(\frac{4}{17}\right)
χ1734(1327,⋅)\chi_{1734}(1327,\cdot) 11 11 e(817)e\left(\frac{8}{17}\right) e(217)e\left(\frac{2}{17}\right) e(617)e\left(\frac{6}{17}\right) e(917)e\left(\frac{9}{17}\right) e(1417)e\left(\frac{14}{17}\right) e(217)e\left(\frac{2}{17}\right) e(1617)e\left(\frac{16}{17}\right) e(617)e\left(\frac{6}{17}\right) e(917)e\left(\frac{9}{17}\right) e(1017)e\left(\frac{10}{17}\right)
χ1734(1429,⋅)\chi_{1734}(1429,\cdot) 11 11 e(617)e\left(\frac{6}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(217)e\left(\frac{2}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(1117)e\left(\frac{11}{17}\right) e(1617)e\left(\frac{16}{17}\right)
χ1734(1531,⋅)\chi_{1734}(1531,\cdot) 11 11 e(417)e\left(\frac{4}{17}\right) e(117)e\left(\frac{1}{17}\right) e(317)e\left(\frac{3}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(717)e\left(\frac{7}{17}\right) e(117)e\left(\frac{1}{17}\right) e(817)e\left(\frac{8}{17}\right) e(317)e\left(\frac{3}{17}\right) e(1317)e\left(\frac{13}{17}\right) e(517)e\left(\frac{5}{17}\right)
χ1734(1633,⋅)\chi_{1734}(1633,\cdot) 11 11 e(217)e\left(\frac{2}{17}\right) e(917)e\left(\frac{9}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1217)e\left(\frac{12}{17}\right) e(917)e\left(\frac{9}{17}\right) e(417)e\left(\frac{4}{17}\right) e(1017)e\left(\frac{10}{17}\right) e(1517)e\left(\frac{15}{17}\right) e(1117)e\left(\frac{11}{17}\right)