Properties

Label 735.bj
Modulus 735735
Conductor 735735
Order 2828
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([14,21,24])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(8,735)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 735735
Conductor: 735735
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: yes
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(ζ28)\Q(\zeta_{28})
Fixed field: Number field defined by a degree 28 polynomial

Characters in Galois orbit

Character 1-1 11 22 44 88 1111 1313 1616 1717 1919 2222 2323
χ735(8,)\chi_{735}(8,\cdot) 11 11 e(1528)e\left(\frac{15}{28}\right) e(114)e\left(\frac{1}{14}\right) e(1728)e\left(\frac{17}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(1528)e\left(\frac{15}{28}\right) e(17)e\left(\frac{1}{7}\right) e(1928)e\left(\frac{19}{28}\right) 1-1 e(928)e\left(\frac{9}{28}\right) e(928)e\left(\frac{9}{28}\right)
χ735(92,)\chi_{735}(92,\cdot) 11 11 e(1328)e\left(\frac{13}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(1128)e\left(\frac{11}{28}\right) e(314)e\left(\frac{3}{14}\right) e(1328)e\left(\frac{13}{28}\right) e(67)e\left(\frac{6}{7}\right) e(928)e\left(\frac{9}{28}\right) 1-1 e(1928)e\left(\frac{19}{28}\right) e(1928)e\left(\frac{19}{28}\right)
χ735(113,)\chi_{735}(113,\cdot) 11 11 e(2328)e\left(\frac{23}{28}\right) e(914)e\left(\frac{9}{14}\right) e(1328)e\left(\frac{13}{28}\right) e(114)e\left(\frac{1}{14}\right) e(2328)e\left(\frac{23}{28}\right) e(27)e\left(\frac{2}{7}\right) e(328)e\left(\frac{3}{28}\right) 1-1 e(2528)e\left(\frac{25}{28}\right) e(2528)e\left(\frac{25}{28}\right)
χ735(218,)\chi_{735}(218,\cdot) 11 11 e(328)e\left(\frac{3}{28}\right) e(314)e\left(\frac{3}{14}\right) e(928)e\left(\frac{9}{28}\right) e(514)e\left(\frac{5}{14}\right) e(328)e\left(\frac{3}{28}\right) e(37)e\left(\frac{3}{7}\right) e(1528)e\left(\frac{15}{28}\right) 1-1 e(1328)e\left(\frac{13}{28}\right) e(1328)e\left(\frac{13}{28}\right)
χ735(302,)\chi_{735}(302,\cdot) 11 11 e(128)e\left(\frac{1}{28}\right) e(114)e\left(\frac{1}{14}\right) e(328)e\left(\frac{3}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(128)e\left(\frac{1}{28}\right) e(17)e\left(\frac{1}{7}\right) e(528)e\left(\frac{5}{28}\right) 1-1 e(2328)e\left(\frac{23}{28}\right) e(2328)e\left(\frac{23}{28}\right)
χ735(323,)\chi_{735}(323,\cdot) 11 11 e(1128)e\left(\frac{11}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(528)e\left(\frac{5}{28}\right) e(914)e\left(\frac{9}{14}\right) e(1128)e\left(\frac{11}{28}\right) e(47)e\left(\frac{4}{7}\right) e(2728)e\left(\frac{27}{28}\right) 1-1 e(128)e\left(\frac{1}{28}\right) e(128)e\left(\frac{1}{28}\right)
χ735(407,)\chi_{735}(407,\cdot) 11 11 e(928)e\left(\frac{9}{28}\right) e(914)e\left(\frac{9}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(114)e\left(\frac{1}{14}\right) e(928)e\left(\frac{9}{28}\right) e(27)e\left(\frac{2}{7}\right) e(1728)e\left(\frac{17}{28}\right) 1-1 e(1128)e\left(\frac{11}{28}\right) e(1128)e\left(\frac{11}{28}\right)
χ735(428,)\chi_{735}(428,\cdot) 11 11 e(1928)e\left(\frac{19}{28}\right) e(514)e\left(\frac{5}{14}\right) e(128)e\left(\frac{1}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(1928)e\left(\frac{19}{28}\right) e(57)e\left(\frac{5}{7}\right) e(1128)e\left(\frac{11}{28}\right) 1-1 e(1728)e\left(\frac{17}{28}\right) e(1728)e\left(\frac{17}{28}\right)
χ735(512,)\chi_{735}(512,\cdot) 11 11 e(1728)e\left(\frac{17}{28}\right) e(314)e\left(\frac{3}{14}\right) e(2328)e\left(\frac{23}{28}\right) e(514)e\left(\frac{5}{14}\right) e(1728)e\left(\frac{17}{28}\right) e(37)e\left(\frac{3}{7}\right) e(128)e\left(\frac{1}{28}\right) 1-1 e(2728)e\left(\frac{27}{28}\right) e(2728)e\left(\frac{27}{28}\right)
χ735(533,)\chi_{735}(533,\cdot) 11 11 e(2728)e\left(\frac{27}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(2528)e\left(\frac{25}{28}\right) e(314)e\left(\frac{3}{14}\right) e(2728)e\left(\frac{27}{28}\right) e(67)e\left(\frac{6}{7}\right) e(2328)e\left(\frac{23}{28}\right) 1-1 e(528)e\left(\frac{5}{28}\right) e(528)e\left(\frac{5}{28}\right)
χ735(617,)\chi_{735}(617,\cdot) 11 11 e(2528)e\left(\frac{25}{28}\right) e(1114)e\left(\frac{11}{14}\right) e(1928)e\left(\frac{19}{28}\right) e(914)e\left(\frac{9}{14}\right) e(2528)e\left(\frac{25}{28}\right) e(47)e\left(\frac{4}{7}\right) e(1328)e\left(\frac{13}{28}\right) 1-1 e(1528)e\left(\frac{15}{28}\right) e(1528)e\left(\frac{15}{28}\right)
χ735(722,)\chi_{735}(722,\cdot) 11 11 e(528)e\left(\frac{5}{28}\right) e(514)e\left(\frac{5}{14}\right) e(1528)e\left(\frac{15}{28}\right) e(1314)e\left(\frac{13}{14}\right) e(528)e\left(\frac{5}{28}\right) e(57)e\left(\frac{5}{7}\right) e(2528)e\left(\frac{25}{28}\right) 1-1 e(328)e\left(\frac{3}{28}\right) e(328)e\left(\frac{3}{28}\right)