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Properties

Label 629.bq
Modulus 629629
Conductor 629629
Order 4848
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(629, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([27,44])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(14,629)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 629629
Conductor: 629629
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4848
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(ζ48)\Q(\zeta_{48})
Fixed field: Number field defined by a degree 48 polynomial

Characters in Galois orbit

Character −1-1 11 22 33 44 55 66 77 88 99 1010 1111
χ629(14,⋅)\chi_{629}(14,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(1948)e\left(\frac{19}{48}\right) e(712)e\left(\frac{7}{12}\right) e(4348)e\left(\frac{43}{48}\right) e(316)e\left(\frac{3}{16}\right) e(2548)e\left(\frac{25}{48}\right) e(38)e\left(\frac{3}{8}\right) e(1924)e\left(\frac{19}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(716)e\left(\frac{7}{16}\right)
χ629(23,⋅)\chi_{629}(23,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(3748)e\left(\frac{37}{48}\right) e(112)e\left(\frac{1}{12}\right) e(1348)e\left(\frac{13}{48}\right) e(516)e\left(\frac{5}{16}\right) e(3148)e\left(\frac{31}{48}\right) e(58)e\left(\frac{5}{8}\right) e(1324)e\left(\frac{13}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(116)e\left(\frac{1}{16}\right)
χ629(29,⋅)\chi_{629}(29,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(4748)e\left(\frac{47}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(2348)e\left(\frac{23}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(2948)e\left(\frac{29}{48}\right) e(78)e\left(\frac{7}{8}\right) e(2324)e\left(\frac{23}{24}\right) e(716)e\left(\frac{7}{16}\right) e(316)e\left(\frac{3}{16}\right)
χ629(45,⋅)\chi_{629}(45,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(2948)e\left(\frac{29}{48}\right) e(512)e\left(\frac{5}{12}\right) e(548)e\left(\frac{5}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(2348)e\left(\frac{23}{48}\right) e(58)e\left(\frac{5}{8}\right) e(524)e\left(\frac{5}{24}\right) e(516)e\left(\frac{5}{16}\right) e(916)e\left(\frac{9}{16}\right)
χ629(88,⋅)\chi_{629}(88,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(4348)e\left(\frac{43}{48}\right) e(712)e\left(\frac{7}{12}\right) e(1948)e\left(\frac{19}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(148)e\left(\frac{1}{48}\right) e(38)e\left(\frac{3}{8}\right) e(1924)e\left(\frac{19}{24}\right) e(316)e\left(\frac{3}{16}\right) e(1516)e\left(\frac{15}{16}\right)
χ629(193,⋅)\chi_{629}(193,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(548)e\left(\frac{5}{48}\right) e(512)e\left(\frac{5}{12}\right) e(2948)e\left(\frac{29}{48}\right) e(516)e\left(\frac{5}{16}\right) e(4748)e\left(\frac{47}{48}\right) e(58)e\left(\frac{5}{8}\right) e(524)e\left(\frac{5}{24}\right) e(1316)e\left(\frac{13}{16}\right) e(116)e\left(\frac{1}{16}\right)
χ629(199,⋅)\chi_{629}(199,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(3148)e\left(\frac{31}{48}\right) e(712)e\left(\frac{7}{12}\right) e(748)e\left(\frac{7}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(1348)e\left(\frac{13}{48}\right) e(78)e\left(\frac{7}{8}\right) e(724)e\left(\frac{7}{24}\right) e(716)e\left(\frac{7}{16}\right) e(316)e\left(\frac{3}{16}\right)
χ629(245,⋅)\chi_{629}(245,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(2548)e\left(\frac{25}{48}\right) e(112)e\left(\frac{1}{12}\right) e(148)e\left(\frac{1}{48}\right) e(916)e\left(\frac{9}{16}\right) e(4348)e\left(\frac{43}{48}\right) e(18)e\left(\frac{1}{8}\right) e(124)e\left(\frac{1}{24}\right) e(116)e\left(\frac{1}{16}\right) e(516)e\left(\frac{5}{16}\right)
χ629(282,⋅)\chi_{629}(282,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(148)e\left(\frac{1}{48}\right) e(112)e\left(\frac{1}{12}\right) e(2548)e\left(\frac{25}{48}\right) e(116)e\left(\frac{1}{16}\right) e(1948)e\left(\frac{19}{48}\right) e(18)e\left(\frac{1}{8}\right) e(124)e\left(\frac{1}{24}\right) e(916)e\left(\frac{9}{16}\right) e(1316)e\left(\frac{13}{16}\right)
χ629(362,⋅)\chi_{629}(362,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(2348)e\left(\frac{23}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(4748)e\left(\frac{47}{48}\right) e(716)e\left(\frac{7}{16}\right) e(548)e\left(\frac{5}{48}\right) e(78)e\left(\frac{7}{8}\right) e(2324)e\left(\frac{23}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(1116)e\left(\frac{11}{16}\right)
χ629(415,⋅)\chi_{629}(415,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(4148)e\left(\frac{41}{48}\right) e(512)e\left(\frac{5}{12}\right) e(1748)e\left(\frac{17}{48}\right) e(916)e\left(\frac{9}{16}\right) e(1148)e\left(\frac{11}{48}\right) e(18)e\left(\frac{1}{8}\right) e(1724)e\left(\frac{17}{24}\right) e(116)e\left(\frac{1}{16}\right) e(516)e\left(\frac{5}{16}\right)
χ629(452,⋅)\chi_{629}(452,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(1748)e\left(\frac{17}{48}\right) e(512)e\left(\frac{5}{12}\right) e(4148)e\left(\frac{41}{48}\right) e(116)e\left(\frac{1}{16}\right) e(3548)e\left(\frac{35}{48}\right) e(18)e\left(\frac{1}{8}\right) e(1724)e\left(\frac{17}{24}\right) e(916)e\left(\frac{9}{16}\right) e(1316)e\left(\frac{13}{16}\right)
χ629(473,⋅)\chi_{629}(473,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(3548)e\left(\frac{35}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(1148)e\left(\frac{11}{48}\right) e(316)e\left(\frac{3}{16}\right) e(4148)e\left(\frac{41}{48}\right) e(38)e\left(\frac{3}{8}\right) e(1124)e\left(\frac{11}{24}\right) e(1116)e\left(\frac{11}{16}\right) e(716)e\left(\frac{7}{16}\right)
χ629(504,⋅)\chi_{629}(504,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(1348)e\left(\frac{13}{48}\right) e(112)e\left(\frac{1}{12}\right) e(3748)e\left(\frac{37}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(748)e\left(\frac{7}{48}\right) e(58)e\left(\frac{5}{8}\right) e(1324)e\left(\frac{13}{24}\right) e(516)e\left(\frac{5}{16}\right) e(916)e\left(\frac{9}{16}\right)
χ629(532,⋅)\chi_{629}(532,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(748)e\left(\frac{7}{48}\right) e(712)e\left(\frac{7}{12}\right) e(3148)e\left(\frac{31}{48}\right) e(716)e\left(\frac{7}{16}\right) e(3748)e\left(\frac{37}{48}\right) e(78)e\left(\frac{7}{8}\right) e(724)e\left(\frac{7}{24}\right) e(1516)e\left(\frac{15}{16}\right) e(1116)e\left(\frac{11}{16}\right)
χ629(547,⋅)\chi_{629}(547,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(1148)e\left(\frac{11}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(3548)e\left(\frac{35}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(1748)e\left(\frac{17}{48}\right) e(38)e\left(\frac{3}{8}\right) e(1124)e\left(\frac{11}{24}\right) e(316)e\left(\frac{3}{16}\right) e(1516)e\left(\frac{15}{16}\right)