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Properties

Modulus 38883888
Structure C2×C2×C324C_{2}\times C_{2}\times C_{324}
Order 12961296

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(3888)
 
pari: g = idealstar(,3888,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1296
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C324C_{2}\times C_{2}\times C_{324}
sage: H.gens()
 
pari: g.gen
 
Generators = χ3888(2431,⋅)\chi_{3888}(2431,\cdot), χ3888(2917,⋅)\chi_{3888}(2917,\cdot), χ3888(1217,⋅)\chi_{3888}(1217,\cdot)

First 32 of 1296 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive −1-1 11 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ3888(1,⋅)\chi_{3888}(1,\cdot) 3888.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ3888(5,⋅)\chi_{3888}(5,\cdot) 3888.cg 324 yes −1-1 11 e(167324)e\left(\frac{167}{324}\right) e(71162)e\left(\frac{71}{162}\right) e(139324)e\left(\frac{139}{324}\right) e(287324)e\left(\frac{287}{324}\right) e(3754)e\left(\frac{37}{54}\right) e(97108)e\left(\frac{97}{108}\right) e(5981)e\left(\frac{59}{81}\right) e(5162)e\left(\frac{5}{162}\right) e(1324)e\left(\frac{1}{324}\right) e(6881)e\left(\frac{68}{81}\right)
χ3888(7,⋅)\chi_{3888}(7,\cdot) 3888.bx 162 no −1-1 11 e(71162)e\left(\frac{71}{162}\right) e(121162)e\left(\frac{121}{162}\right) e(2381)e\left(\frac{23}{81}\right) e(155162)e\left(\frac{155}{162}\right) e(727)e\left(\frac{7}{27}\right) e(1127)e\left(\frac{11}{27}\right) e(95162)e\left(\frac{95}{162}\right) e(7181)e\left(\frac{71}{81}\right) e(79162)e\left(\frac{79}{162}\right) e(23162)e\left(\frac{23}{162}\right)
χ3888(11,⋅)\chi_{3888}(11,\cdot) 3888.ch 324 yes 11 11 e(139324)e\left(\frac{139}{324}\right) e(2381)e\left(\frac{23}{81}\right) e(41324)e\left(\frac{41}{324}\right) e(235324)e\left(\frac{235}{324}\right) e(3554)e\left(\frac{35}{54}\right) e(83108)e\left(\frac{83}{108}\right) e(89162)e\left(\frac{89}{162}\right) e(139162)e\left(\frac{139}{162}\right) e(125324)e\left(\frac{125}{324}\right) e(71162)e\left(\frac{71}{162}\right)
χ3888(13,⋅)\chi_{3888}(13,\cdot) 3888.ce 324 yes 11 11 e(287324)e\left(\frac{287}{324}\right) e(155162)e\left(\frac{155}{162}\right) e(235324)e\left(\frac{235}{324}\right) e(209324)e\left(\frac{209}{324}\right) e(1727)e\left(\frac{17}{27}\right) e(103108)e\left(\frac{103}{108}\right) e(115162)e\left(\frac{115}{162}\right) e(125162)e\left(\frac{125}{162}\right) e(25324)e\left(\frac{25}{324}\right) e(8081)e\left(\frac{80}{81}\right)
χ3888(17,⋅)\chi_{3888}(17,\cdot) 3888.bo 54 no −1-1 11 e(3754)e\left(\frac{37}{54}\right) e(727)e\left(\frac{7}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1354)e\left(\frac{13}{54}\right) e(1027)e\left(\frac{10}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(227)e\left(\frac{2}{27}\right)
χ3888(19,⋅)\chi_{3888}(19,\cdot) 3888.bu 108 no −1-1 11 e(97108)e\left(\frac{97}{108}\right) e(1127)e\left(\frac{11}{27}\right) e(83108)e\left(\frac{83}{108}\right) e(103108)e\left(\frac{103}{108}\right) e(79)e\left(\frac{7}{9}\right) e(3536)e\left(\frac{35}{36}\right) e(1627)e\left(\frac{16}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(95108)e\left(\frac{95}{108}\right) e(4154)e\left(\frac{41}{54}\right)
χ3888(23,⋅)\chi_{3888}(23,\cdot) 3888.cb 162 no 11 11 e(5981)e\left(\frac{59}{81}\right) e(95162)e\left(\frac{95}{162}\right) e(89162)e\left(\frac{89}{162}\right) e(115162)e\left(\frac{115}{162}\right) e(1354)e\left(\frac{13}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(4781)e\left(\frac{47}{81}\right) e(3781)e\left(\frac{37}{81}\right) e(2881)e\left(\frac{28}{81}\right) e(85162)e\left(\frac{85}{162}\right)
χ3888(25,⋅)\chi_{3888}(25,\cdot) 3888.bz 162 no 11 11 e(5162)e\left(\frac{5}{162}\right) e(7181)e\left(\frac{71}{81}\right) e(139162)e\left(\frac{139}{162}\right) e(125162)e\left(\frac{125}{162}\right) e(1027)e\left(\frac{10}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(3781)e\left(\frac{37}{81}\right) e(581)e\left(\frac{5}{81}\right) e(1162)e\left(\frac{1}{162}\right) e(5581)e\left(\frac{55}{81}\right)
χ3888(29,⋅)\chi_{3888}(29,\cdot) 3888.cg 324 yes −1-1 11 e(1324)e\left(\frac{1}{324}\right) e(79162)e\left(\frac{79}{162}\right) e(125324)e\left(\frac{125}{324}\right) e(25324)e\left(\frac{25}{324}\right) e(2954)e\left(\frac{29}{54}\right) e(95108)e\left(\frac{95}{108}\right) e(2881)e\left(\frac{28}{81}\right) e(1162)e\left(\frac{1}{162}\right) e(227324)e\left(\frac{227}{324}\right) e(4681)e\left(\frac{46}{81}\right)
χ3888(31,⋅)\chi_{3888}(31,\cdot) 3888.by 162 no −1-1 11 e(6881)e\left(\frac{68}{81}\right) e(23162)e\left(\frac{23}{162}\right) e(71162)e\left(\frac{71}{162}\right) e(8081)e\left(\frac{80}{81}\right) e(227)e\left(\frac{2}{27}\right) e(4154)e\left(\frac{41}{54}\right) e(85162)e\left(\frac{85}{162}\right) e(5581)e\left(\frac{55}{81}\right) e(4681)e\left(\frac{46}{81}\right) e(157162)e\left(\frac{157}{162}\right)
χ3888(35,⋅)\chi_{3888}(35,\cdot) 3888.bt 108 no 11 11 e(103108)e\left(\frac{103}{108}\right) e(527)e\left(\frac{5}{27}\right) e(77108)e\left(\frac{77}{108}\right) e(91108)e\left(\frac{91}{108}\right) e(1718)e\left(\frac{17}{18}\right) e(1136)e\left(\frac{11}{36}\right) e(1754)e\left(\frac{17}{54}\right) e(4954)e\left(\frac{49}{54}\right) e(53108)e\left(\frac{53}{108}\right) e(5354)e\left(\frac{53}{54}\right)
χ3888(37,⋅)\chi_{3888}(37,\cdot) 3888.bw 108 no 11 11 e(95108)e\left(\frac{95}{108}\right) e(5354)e\left(\frac{53}{54}\right) e(103108)e\left(\frac{103}{108}\right) e(53108)e\left(\frac{53}{108}\right) e(59)e\left(\frac{5}{9}\right) e(736)e\left(\frac{7}{36}\right) e(154)e\left(\frac{1}{54}\right) e(4154)e\left(\frac{41}{54}\right) e(73108)e\left(\frac{73}{108}\right) e(2327)e\left(\frac{23}{27}\right)
χ3888(41,⋅)\chi_{3888}(41,\cdot) 3888.cd 162 no −1-1 11 e(281)e\left(\frac{2}{81}\right) e(7381)e\left(\frac{73}{81}\right) e(781)e\left(\frac{7}{81}\right) e(19162)e\left(\frac{19}{162}\right) e(4354)e\left(\frac{43}{54}\right) e(2954)e\left(\frac{29}{54}\right) e(43162)e\left(\frac{43}{162}\right) e(481)e\left(\frac{4}{81}\right) e(4981)e\left(\frac{49}{81}\right) e(4481)e\left(\frac{44}{81}\right)
χ3888(43,⋅)\chi_{3888}(43,\cdot) 3888.cf 324 yes −1-1 11 e(229324)e\left(\frac{229}{324}\right) e(1481)e\left(\frac{14}{81}\right) e(275324)e\left(\frac{275}{324}\right) e(55324)e\left(\frac{55}{324}\right) e(1327)e\left(\frac{13}{27}\right) e(47108)e\left(\frac{47}{108}\right) e(1381)e\left(\frac{13}{81}\right) e(67162)e\left(\frac{67}{162}\right) e(143324)e\left(\frac{143}{324}\right) e(89162)e\left(\frac{89}{162}\right)
χ3888(47,⋅)\chi_{3888}(47,\cdot) 3888.cc 162 no 11 11 e(107162)e\left(\frac{107}{162}\right) e(139162)e\left(\frac{139}{162}\right) e(581)e\left(\frac{5}{81}\right) e(181)e\left(\frac{1}{81}\right) e(2354)e\left(\frac{23}{54}\right) e(1354)e\left(\frac{13}{54}\right) e(7981)e\left(\frac{79}{81}\right) e(2681)e\left(\frac{26}{81}\right) e(151162)e\left(\frac{151}{162}\right) e(5162)e\left(\frac{5}{162}\right)
χ3888(49,⋅)\chi_{3888}(49,\cdot) 3888.bs 81 no 11 11 e(7181)e\left(\frac{71}{81}\right) e(4081)e\left(\frac{40}{81}\right) e(4681)e\left(\frac{46}{81}\right) e(7481)e\left(\frac{74}{81}\right) e(1427)e\left(\frac{14}{27}\right) e(2227)e\left(\frac{22}{27}\right) e(1481)e\left(\frac{14}{81}\right) e(6181)e\left(\frac{61}{81}\right) e(7981)e\left(\frac{79}{81}\right) e(2381)e\left(\frac{23}{81}\right)
χ3888(53,⋅)\chi_{3888}(53,\cdot) 3888.bj 36 no −1-1 11 e(1136)e\left(\frac{11}{36}\right) e(518)e\left(\frac{5}{18}\right) e(736)e\left(\frac{7}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) e(29)e\left(\frac{2}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(1336)e\left(\frac{13}{36}\right) e(29)e\left(\frac{2}{9}\right)
χ3888(55,⋅)\chi_{3888}(55,\cdot) 3888.z 18 no −1-1 11 e(1718)e\left(\frac{17}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(59)e\left(\frac{5}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(718)e\left(\frac{7}{18}\right) e(518)e\left(\frac{5}{18}\right)
χ3888(59,⋅)\chi_{3888}(59,\cdot) 3888.ch 324 yes 11 11 e(131324)e\left(\frac{131}{324}\right) e(3181)e\left(\frac{31}{81}\right) e(13324)e\left(\frac{13}{324}\right) e(35324)e\left(\frac{35}{324}\right) e(1954)e\left(\frac{19}{54}\right) e(79108)e\left(\frac{79}{108}\right) e(127162)e\left(\frac{127}{162}\right) e(131162)e\left(\frac{131}{162}\right) e(253324)e\left(\frac{253}{324}\right) e(145162)e\left(\frac{145}{162}\right)
χ3888(61,⋅)\chi_{3888}(61,\cdot) 3888.ce 324 yes 11 11 e(151324)e\left(\frac{151}{324}\right) e(103162)e\left(\frac{103}{162}\right) e(83324)e\left(\frac{83}{324}\right) e(49324)e\left(\frac{49}{324}\right) e(1627)e\left(\frac{16}{27}\right) e(35108)e\left(\frac{35}{108}\right) e(113162)e\left(\frac{113}{162}\right) e(151162)e\left(\frac{151}{162}\right) e(257324)e\left(\frac{257}{324}\right) e(6181)e\left(\frac{61}{81}\right)
χ3888(65,⋅)\chi_{3888}(65,\cdot) 3888.ca 162 no −1-1 11 e(65162)e\left(\frac{65}{162}\right) e(3281)e\left(\frac{32}{81}\right) e(25162)e\left(\frac{25}{162}\right) e(4381)e\left(\frac{43}{81}\right) e(1754)e\left(\frac{17}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(71162)e\left(\frac{71}{162}\right) e(6581)e\left(\frac{65}{81}\right) e(13162)e\left(\frac{13}{162}\right) e(6781)e\left(\frac{67}{81}\right)
χ3888(67,⋅)\chi_{3888}(67,\cdot) 3888.cf 324 yes −1-1 11 e(323324)e\left(\frac{323}{324}\right) e(181)e\left(\frac{1}{81}\right) e(37324)e\left(\frac{37}{324}\right) e(137324)e\left(\frac{137}{324}\right) e(2627)e\left(\frac{26}{27}\right) e(13108)e\left(\frac{13}{108}\right) e(5381)e\left(\frac{53}{81}\right) e(161162)e\left(\frac{161}{162}\right) e(97324)e\left(\frac{97}{324}\right) e(151162)e\left(\frac{151}{162}\right)
χ3888(71,⋅)\chi_{3888}(71,\cdot) 3888.bn 54 no 11 11 e(2027)e\left(\frac{20}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(554)e\left(\frac{5}{54}\right) e(154)e\left(\frac{1}{54}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(2627)e\left(\frac{26}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(427)e\left(\frac{4}{27}\right) e(4354)e\left(\frac{43}{54}\right)
χ3888(73,⋅)\chi_{3888}(73,\cdot) 3888.bp 54 no 11 11 e(554)e\left(\frac{5}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(3154)e\left(\frac{31}{54}\right) e(1754)e\left(\frac{17}{54}\right) e(19)e\left(\frac{1}{9}\right) e(718)e\left(\frac{7}{18}\right) e(1027)e\left(\frac{10}{27}\right) e(527)e\left(\frac{5}{27}\right) e(154)e\left(\frac{1}{54}\right) e(127)e\left(\frac{1}{27}\right)
χ3888(77,⋅)\chi_{3888}(77,\cdot) 3888.cg 324 yes −1-1 11 e(281324)e\left(\frac{281}{324}\right) e(5162)e\left(\frac{5}{162}\right) e(133324)e\left(\frac{133}{324}\right) e(221324)e\left(\frac{221}{324}\right) e(4954)e\left(\frac{49}{54}\right) e(19108)e\left(\frac{19}{108}\right) e(1181)e\left(\frac{11}{81}\right) e(119162)e\left(\frac{119}{162}\right) e(283324)e\left(\frac{283}{324}\right) e(4781)e\left(\frac{47}{81}\right)
χ3888(79,⋅)\chi_{3888}(79,\cdot) 3888.by 162 no −1-1 11 e(2581)e\left(\frac{25}{81}\right) e(43162)e\left(\frac{43}{162}\right) e(13162)e\left(\frac{13}{162}\right) e(5881)e\left(\frac{58}{81}\right) e(1927)e\left(\frac{19}{27}\right) e(2554)e\left(\frac{25}{54}\right) e(11162)e\left(\frac{11}{162}\right) e(5081)e\left(\frac{50}{81}\right) e(581)e\left(\frac{5}{81}\right) e(47162)e\left(\frac{47}{162}\right)
χ3888(83,⋅)\chi_{3888}(83,\cdot) 3888.ch 324 yes 11 11 e(73324)e\left(\frac{73}{324}\right) e(881)e\left(\frac{8}{81}\right) e(215324)e\left(\frac{215}{324}\right) e(205324)e\left(\frac{205}{324}\right) e(1154)e\left(\frac{11}{54}\right) e(77108)e\left(\frac{77}{108}\right) e(119162)e\left(\frac{119}{162}\right) e(73162)e\left(\frac{73}{162}\right) e(47324)e\left(\frac{47}{324}\right) e(155162)e\left(\frac{155}{162}\right)
χ3888(85,⋅)\chi_{3888}(85,\cdot) 3888.ce 324 yes 11 11 e(65324)e\left(\frac{65}{324}\right) e(113162)e\left(\frac{113}{162}\right) e(25324)e\left(\frac{25}{324}\right) e(167324)e\left(\frac{167}{324}\right) e(1127)e\left(\frac{11}{27}\right) e(73108)e\left(\frac{73}{108}\right) e(157162)e\left(\frac{157}{162}\right) e(65162)e\left(\frac{65}{162}\right) e(175324)e\left(\frac{175}{324}\right) e(7481)e\left(\frac{74}{81}\right)
χ3888(89,⋅)\chi_{3888}(89,\cdot) 3888.bl 54 no −1-1 11 e(727)e\left(\frac{7}{27}\right) e(2627)e\left(\frac{26}{27}\right) e(1127)e\left(\frac{11}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(1118)e\left(\frac{11}{18}\right) e(718)e\left(\frac{7}{18}\right) e(2954)e\left(\frac{29}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(2327)e\left(\frac{23}{27}\right) e(1927)e\left(\frac{19}{27}\right)
χ3888(91,⋅)\chi_{3888}(91,\cdot) 3888.bu 108 no −1-1 11 e(35108)e\left(\frac{35}{108}\right) e(1927)e\left(\frac{19}{27}\right) e(1108)e\left(\frac{1}{108}\right) e(65108)e\left(\frac{65}{108}\right) e(89)e\left(\frac{8}{9}\right) e(1336)e\left(\frac{13}{36}\right) e(827)e\left(\frac{8}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(61108)e\left(\frac{61}{108}\right) e(754)e\left(\frac{7}{54}\right)
χ3888(95,⋅)\chi_{3888}(95,\cdot) 3888.cc 162 no 11 11 e(67162)e\left(\frac{67}{162}\right) e(137162)e\left(\frac{137}{162}\right) e(1681)e\left(\frac{16}{81}\right) e(6881)e\left(\frac{68}{81}\right) e(2554)e\left(\frac{25}{54}\right) e(4754)e\left(\frac{47}{54}\right) e(2681)e\left(\frac{26}{81}\right) e(6781)e\left(\frac{67}{81}\right) e(143162)e\left(\frac{143}{162}\right) e(97162)e\left(\frac{97}{162}\right)
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