Properties

Label 1152.bv
Modulus 11521152
Conductor 11521152
Order 9696
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(1152, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([0,45,32])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(13,1152)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 11521152
Conductor: 11521152
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 9696
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(ζ96)\Q(\zeta_{96})
Fixed field: Number field defined by a degree 96 polynomial

First 31 of 32 characters in Galois orbit

Character 1-1 11 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ1152(13,)\chi_{1152}(13,\cdot) 11 11 e(1396)e\left(\frac{13}{96}\right) e(148)e\left(\frac{1}{48}\right) e(1796)e\left(\frac{17}{96}\right) e(6796)e\left(\frac{67}{96}\right) e(18)e\left(\frac{1}{8}\right) e(2532)e\left(\frac{25}{32}\right) e(1148)e\left(\frac{11}{48}\right) e(1348)e\left(\frac{13}{48}\right) e(9596)e\left(\frac{95}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(61,)\chi_{1152}(61,\cdot) 11 11 e(8996)e\left(\frac{89}{96}\right) e(2948)e\left(\frac{29}{48}\right) e(1396)e\left(\frac{13}{96}\right) e(2396)e\left(\frac{23}{96}\right) e(58)e\left(\frac{5}{8}\right) e(2132)e\left(\frac{21}{32}\right) e(3148)e\left(\frac{31}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(6796)e\left(\frac{67}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(85,)\chi_{1152}(85,\cdot) 11 11 e(5596)e\left(\frac{55}{96}\right) e(1948)e\left(\frac{19}{48}\right) e(3596)e\left(\frac{35}{96}\right) e(2596)e\left(\frac{25}{96}\right) e(38)e\left(\frac{3}{8}\right) e(2732)e\left(\frac{27}{32}\right) e(1748)e\left(\frac{17}{48}\right) e(748)e\left(\frac{7}{48}\right) e(7796)e\left(\frac{77}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(133,)\chi_{1152}(133,\cdot) 11 11 e(3596)e\left(\frac{35}{96}\right) e(4748)e\left(\frac{47}{48}\right) e(3196)e\left(\frac{31}{96}\right) e(7796)e\left(\frac{77}{96}\right) e(78)e\left(\frac{7}{8}\right) e(2332)e\left(\frac{23}{32}\right) e(3748)e\left(\frac{37}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(4996)e\left(\frac{49}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(157,)\chi_{1152}(157,\cdot) 11 11 e(4996)e\left(\frac{49}{96}\right) e(3748)e\left(\frac{37}{48}\right) e(596)e\left(\frac{5}{96}\right) e(3196)e\left(\frac{31}{96}\right) e(58)e\left(\frac{5}{8}\right) e(1332)e\left(\frac{13}{32}\right) e(2348)e\left(\frac{23}{48}\right) e(148)e\left(\frac{1}{48}\right) e(1196)e\left(\frac{11}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(205,)\chi_{1152}(205,\cdot) 11 11 e(2996)e\left(\frac{29}{96}\right) e(1748)e\left(\frac{17}{48}\right) e(196)e\left(\frac{1}{96}\right) e(8396)e\left(\frac{83}{96}\right) e(18)e\left(\frac{1}{8}\right) e(932)e\left(\frac{9}{32}\right) e(4348)e\left(\frac{43}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(7996)e\left(\frac{79}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(229,)\chi_{1152}(229,\cdot) 11 11 e(9196)e\left(\frac{91}{96}\right) e(748)e\left(\frac{7}{48}\right) e(2396)e\left(\frac{23}{96}\right) e(8596)e\left(\frac{85}{96}\right) e(78)e\left(\frac{7}{8}\right) e(1532)e\left(\frac{15}{32}\right) e(2948)e\left(\frac{29}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(8996)e\left(\frac{89}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(277,)\chi_{1152}(277,\cdot) 11 11 e(7196)e\left(\frac{71}{96}\right) e(3548)e\left(\frac{35}{48}\right) e(1996)e\left(\frac{19}{96}\right) e(4196)e\left(\frac{41}{96}\right) e(38)e\left(\frac{3}{8}\right) e(1132)e\left(\frac{11}{32}\right) e(148)e\left(\frac{1}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(6196)e\left(\frac{61}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(301,)\chi_{1152}(301,\cdot) 11 11 e(8596)e\left(\frac{85}{96}\right) e(2548)e\left(\frac{25}{48}\right) e(8996)e\left(\frac{89}{96}\right) e(9196)e\left(\frac{91}{96}\right) e(18)e\left(\frac{1}{8}\right) e(132)e\left(\frac{1}{32}\right) e(3548)e\left(\frac{35}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(2396)e\left(\frac{23}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(349,)\chi_{1152}(349,\cdot) 11 11 e(6596)e\left(\frac{65}{96}\right) e(548)e\left(\frac{5}{48}\right) e(8596)e\left(\frac{85}{96}\right) e(4796)e\left(\frac{47}{96}\right) e(58)e\left(\frac{5}{8}\right) e(2932)e\left(\frac{29}{32}\right) e(748)e\left(\frac{7}{48}\right) e(1748)e\left(\frac{17}{48}\right) e(9196)e\left(\frac{91}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(373,)\chi_{1152}(373,\cdot) 11 11 e(3196)e\left(\frac{31}{96}\right) e(4348)e\left(\frac{43}{48}\right) e(1196)e\left(\frac{11}{96}\right) e(4996)e\left(\frac{49}{96}\right) e(38)e\left(\frac{3}{8}\right) e(332)e\left(\frac{3}{32}\right) e(4148)e\left(\frac{41}{48}\right) e(3148)e\left(\frac{31}{48}\right) e(596)e\left(\frac{5}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(421,)\chi_{1152}(421,\cdot) 11 11 e(1196)e\left(\frac{11}{96}\right) e(2348)e\left(\frac{23}{48}\right) e(796)e\left(\frac{7}{96}\right) e(596)e\left(\frac{5}{96}\right) e(78)e\left(\frac{7}{8}\right) e(3132)e\left(\frac{31}{32}\right) e(1348)e\left(\frac{13}{48}\right) e(1148)e\left(\frac{11}{48}\right) e(7396)e\left(\frac{73}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(445,)\chi_{1152}(445,\cdot) 11 11 e(2596)e\left(\frac{25}{96}\right) e(1348)e\left(\frac{13}{48}\right) e(7796)e\left(\frac{77}{96}\right) e(5596)e\left(\frac{55}{96}\right) e(58)e\left(\frac{5}{8}\right) e(2132)e\left(\frac{21}{32}\right) e(4748)e\left(\frac{47}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(3596)e\left(\frac{35}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(493,)\chi_{1152}(493,\cdot) 11 11 e(596)e\left(\frac{5}{96}\right) e(4148)e\left(\frac{41}{48}\right) e(7396)e\left(\frac{73}{96}\right) e(1196)e\left(\frac{11}{96}\right) e(18)e\left(\frac{1}{8}\right) e(1732)e\left(\frac{17}{32}\right) e(1948)e\left(\frac{19}{48}\right) e(548)e\left(\frac{5}{48}\right) e(796)e\left(\frac{7}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(517,)\chi_{1152}(517,\cdot) 11 11 e(6796)e\left(\frac{67}{96}\right) e(3148)e\left(\frac{31}{48}\right) e(9596)e\left(\frac{95}{96}\right) e(1396)e\left(\frac{13}{96}\right) e(78)e\left(\frac{7}{8}\right) e(2332)e\left(\frac{23}{32}\right) e(548)e\left(\frac{5}{48}\right) e(1948)e\left(\frac{19}{48}\right) e(1796)e\left(\frac{17}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(565,)\chi_{1152}(565,\cdot) 11 11 e(4796)e\left(\frac{47}{96}\right) e(1148)e\left(\frac{11}{48}\right) e(9196)e\left(\frac{91}{96}\right) e(6596)e\left(\frac{65}{96}\right) e(38)e\left(\frac{3}{8}\right) e(1932)e\left(\frac{19}{32}\right) e(2548)e\left(\frac{25}{48}\right) e(4748)e\left(\frac{47}{48}\right) e(8596)e\left(\frac{85}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(589,)\chi_{1152}(589,\cdot) 11 11 e(6196)e\left(\frac{61}{96}\right) e(148)e\left(\frac{1}{48}\right) e(6596)e\left(\frac{65}{96}\right) e(1996)e\left(\frac{19}{96}\right) e(18)e\left(\frac{1}{8}\right) e(932)e\left(\frac{9}{32}\right) e(1148)e\left(\frac{11}{48}\right) e(1348)e\left(\frac{13}{48}\right) e(4796)e\left(\frac{47}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(637,)\chi_{1152}(637,\cdot) 11 11 e(4196)e\left(\frac{41}{96}\right) e(2948)e\left(\frac{29}{48}\right) e(6196)e\left(\frac{61}{96}\right) e(7196)e\left(\frac{71}{96}\right) e(58)e\left(\frac{5}{8}\right) e(532)e\left(\frac{5}{32}\right) e(3148)e\left(\frac{31}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(1996)e\left(\frac{19}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(661,)\chi_{1152}(661,\cdot) 11 11 e(796)e\left(\frac{7}{96}\right) e(1948)e\left(\frac{19}{48}\right) e(8396)e\left(\frac{83}{96}\right) e(7396)e\left(\frac{73}{96}\right) e(38)e\left(\frac{3}{8}\right) e(1132)e\left(\frac{11}{32}\right) e(1748)e\left(\frac{17}{48}\right) e(748)e\left(\frac{7}{48}\right) e(2996)e\left(\frac{29}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(709,)\chi_{1152}(709,\cdot) 11 11 e(8396)e\left(\frac{83}{96}\right) e(4748)e\left(\frac{47}{48}\right) e(7996)e\left(\frac{79}{96}\right) e(2996)e\left(\frac{29}{96}\right) e(78)e\left(\frac{7}{8}\right) e(732)e\left(\frac{7}{32}\right) e(3748)e\left(\frac{37}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(196)e\left(\frac{1}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(733,)\chi_{1152}(733,\cdot) 11 11 e(196)e\left(\frac{1}{96}\right) e(3748)e\left(\frac{37}{48}\right) e(5396)e\left(\frac{53}{96}\right) e(7996)e\left(\frac{79}{96}\right) e(58)e\left(\frac{5}{8}\right) e(2932)e\left(\frac{29}{32}\right) e(2348)e\left(\frac{23}{48}\right) e(148)e\left(\frac{1}{48}\right) e(5996)e\left(\frac{59}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(781,)\chi_{1152}(781,\cdot) 11 11 e(7796)e\left(\frac{77}{96}\right) e(1748)e\left(\frac{17}{48}\right) e(4996)e\left(\frac{49}{96}\right) e(3596)e\left(\frac{35}{96}\right) e(18)e\left(\frac{1}{8}\right) e(2532)e\left(\frac{25}{32}\right) e(4348)e\left(\frac{43}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(3196)e\left(\frac{31}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(805,)\chi_{1152}(805,\cdot) 11 11 e(4396)e\left(\frac{43}{96}\right) e(748)e\left(\frac{7}{48}\right) e(7196)e\left(\frac{71}{96}\right) e(3796)e\left(\frac{37}{96}\right) e(78)e\left(\frac{7}{8}\right) e(3132)e\left(\frac{31}{32}\right) e(2948)e\left(\frac{29}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(4196)e\left(\frac{41}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(853,)\chi_{1152}(853,\cdot) 11 11 e(2396)e\left(\frac{23}{96}\right) e(3548)e\left(\frac{35}{48}\right) e(6796)e\left(\frac{67}{96}\right) e(8996)e\left(\frac{89}{96}\right) e(38)e\left(\frac{3}{8}\right) e(2732)e\left(\frac{27}{32}\right) e(148)e\left(\frac{1}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(1396)e\left(\frac{13}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(877,)\chi_{1152}(877,\cdot) 11 11 e(3796)e\left(\frac{37}{96}\right) e(2548)e\left(\frac{25}{48}\right) e(4196)e\left(\frac{41}{96}\right) e(4396)e\left(\frac{43}{96}\right) e(18)e\left(\frac{1}{8}\right) e(1732)e\left(\frac{17}{32}\right) e(3548)e\left(\frac{35}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(7196)e\left(\frac{71}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(925,)\chi_{1152}(925,\cdot) 11 11 e(1796)e\left(\frac{17}{96}\right) e(548)e\left(\frac{5}{48}\right) e(3796)e\left(\frac{37}{96}\right) e(9596)e\left(\frac{95}{96}\right) e(58)e\left(\frac{5}{8}\right) e(1332)e\left(\frac{13}{32}\right) e(748)e\left(\frac{7}{48}\right) e(1748)e\left(\frac{17}{48}\right) e(4396)e\left(\frac{43}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(949,)\chi_{1152}(949,\cdot) 11 11 e(7996)e\left(\frac{79}{96}\right) e(4348)e\left(\frac{43}{48}\right) e(5996)e\left(\frac{59}{96}\right) e(196)e\left(\frac{1}{96}\right) e(38)e\left(\frac{3}{8}\right) e(1932)e\left(\frac{19}{32}\right) e(4148)e\left(\frac{41}{48}\right) e(3148)e\left(\frac{31}{48}\right) e(5396)e\left(\frac{53}{96}\right) e(1112)e\left(\frac{11}{12}\right)
χ1152(997,)\chi_{1152}(997,\cdot) 11 11 e(5996)e\left(\frac{59}{96}\right) e(2348)e\left(\frac{23}{48}\right) e(5596)e\left(\frac{55}{96}\right) e(5396)e\left(\frac{53}{96}\right) e(78)e\left(\frac{7}{8}\right) e(1532)e\left(\frac{15}{32}\right) e(1348)e\left(\frac{13}{48}\right) e(1148)e\left(\frac{11}{48}\right) e(2596)e\left(\frac{25}{96}\right) e(712)e\left(\frac{7}{12}\right)
χ1152(1021,)\chi_{1152}(1021,\cdot) 11 11 e(7396)e\left(\frac{73}{96}\right) e(1348)e\left(\frac{13}{48}\right) e(2996)e\left(\frac{29}{96}\right) e(796)e\left(\frac{7}{96}\right) e(58)e\left(\frac{5}{8}\right) e(532)e\left(\frac{5}{32}\right) e(4748)e\left(\frac{47}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(8396)e\left(\frac{83}{96}\right) e(512)e\left(\frac{5}{12}\right)
χ1152(1069,)\chi_{1152}(1069,\cdot) 11 11 e(5396)e\left(\frac{53}{96}\right) e(4148)e\left(\frac{41}{48}\right) e(2596)e\left(\frac{25}{96}\right) e(5996)e\left(\frac{59}{96}\right) e(18)e\left(\frac{1}{8}\right) e(132)e\left(\frac{1}{32}\right) e(1948)e\left(\frac{19}{48}\right) e(548)e\left(\frac{5}{48}\right) e(5596)e\left(\frac{55}{96}\right) e(112)e\left(\frac{1}{12}\right)
χ1152(1093,)\chi_{1152}(1093,\cdot) 11 11 e(1996)e\left(\frac{19}{96}\right) e(3148)e\left(\frac{31}{48}\right) e(4796)e\left(\frac{47}{96}\right) e(6196)e\left(\frac{61}{96}\right) e(78)e\left(\frac{7}{8}\right) e(732)e\left(\frac{7}{32}\right) e(548)e\left(\frac{5}{48}\right) e(1948)e\left(\frac{19}{48}\right) e(6596)e\left(\frac{65}{96}\right) e(1112)e\left(\frac{11}{12}\right)