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Properties

Modulus 87888788
Structure C2×C2028C_{2}\times C_{2028}
Order 40564056

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(8788)
 
pari: g = idealstar(,8788,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4056
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2028C_{2}\times C_{2028}
sage: H.gens()
 
pari: g.gen
 
Generators = χ8788(4395,⋅)\chi_{8788}(4395,\cdot), χ8788(6593,⋅)\chi_{8788}(6593,\cdot)

First 32 of 4056 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 33 55 77 99 1111 1515 1717 1919 2121 2323
χ8788(1,⋅)\chi_{8788}(1,\cdot) 8788.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ8788(3,⋅)\chi_{8788}(3,\cdot) 8788.bf 1014 yes −1-1 11 e(51014)e\left(\frac{5}{1014}\right) e(93169)e\left(\frac{93}{169}\right) e(1991014)e\left(\frac{199}{1014}\right) e(5507)e\left(\frac{5}{507}\right) e(9651014)e\left(\frac{965}{1014}\right) e(5631014)e\left(\frac{563}{1014}\right) e(158507)e\left(\frac{158}{507}\right) e(3178)e\left(\frac{31}{78}\right) e(34169)e\left(\frac{34}{169}\right) e(4178)e\left(\frac{41}{78}\right)
χ8788(5,⋅)\chi_{8788}(5,\cdot) 8788.be 676 no −1-1 11 e(93169)e\left(\frac{93}{169}\right) e(651676)e\left(\frac{651}{676}\right) e(373676)e\left(\frac{373}{676}\right) e(17169)e\left(\frac{17}{169}\right) e(309676)e\left(\frac{309}{676}\right) e(347676)e\left(\frac{347}{676}\right) e(297338)e\left(\frac{297}{338}\right) e(4752)e\left(\frac{47}{52}\right) e(69676)e\left(\frac{69}{676}\right) e(2526)e\left(\frac{25}{26}\right)
χ8788(7,⋅)\chi_{8788}(7,\cdot) 8788.bj 2028 yes 11 11 e(1991014)e\left(\frac{199}{1014}\right) e(373676)e\left(\frac{373}{676}\right) e(15432028)e\left(\frac{1543}{2028}\right) e(199507)e\left(\frac{199}{507}\right) e(12712028)e\left(\frac{1271}{2028}\right) e(15172028)e\left(\frac{1517}{2028}\right) e(7131014)e\left(\frac{713}{1014}\right) e(73156)e\left(\frac{73}{156}\right) e(647676)e\left(\frac{647}{676}\right) e(3239)e\left(\frac{32}{39}\right)
χ8788(9,⋅)\chi_{8788}(9,\cdot) 8788.bc 507 no 11 11 e(5507)e\left(\frac{5}{507}\right) e(17169)e\left(\frac{17}{169}\right) e(199507)e\left(\frac{199}{507}\right) e(10507)e\left(\frac{10}{507}\right) e(458507)e\left(\frac{458}{507}\right) e(56507)e\left(\frac{56}{507}\right) e(316507)e\left(\frac{316}{507}\right) e(3139)e\left(\frac{31}{39}\right) e(68169)e\left(\frac{68}{169}\right) e(239)e\left(\frac{2}{39}\right)
χ8788(11,⋅)\chi_{8788}(11,\cdot) 8788.bj 2028 yes 11 11 e(9651014)e\left(\frac{965}{1014}\right) e(309676)e\left(\frac{309}{676}\right) e(12712028)e\left(\frac{1271}{2028}\right) e(458507)e\left(\frac{458}{507}\right) e(8592028)e\left(\frac{859}{2028}\right) e(8292028)e\left(\frac{829}{2028}\right) e(6551014)e\left(\frac{655}{1014}\right) e(149156)e\left(\frac{149}{156}\right) e(391676)e\left(\frac{391}{676}\right) e(3739)e\left(\frac{37}{39}\right)
χ8788(15,⋅)\chi_{8788}(15,\cdot) 8788.bj 2028 yes 11 11 e(5631014)e\left(\frac{563}{1014}\right) e(347676)e\left(\frac{347}{676}\right) e(15172028)e\left(\frac{1517}{2028}\right) e(56507)e\left(\frac{56}{507}\right) e(8292028)e\left(\frac{829}{2028}\right) e(1392028)e\left(\frac{139}{2028}\right) e(1931014)e\left(\frac{193}{1014}\right) e(47156)e\left(\frac{47}{156}\right) e(205676)e\left(\frac{205}{676}\right) e(1939)e\left(\frac{19}{39}\right)
χ8788(17,⋅)\chi_{8788}(17,\cdot) 8788.bg 1014 no 11 11 e(158507)e\left(\frac{158}{507}\right) e(297338)e\left(\frac{297}{338}\right) e(7131014)e\left(\frac{713}{1014}\right) e(316507)e\left(\frac{316}{507}\right) e(6551014)e\left(\frac{655}{1014}\right) e(1931014)e\left(\frac{193}{1014}\right) e(454507)e\left(\frac{454}{507}\right) e(1778)e\left(\frac{17}{78}\right) e(5338)e\left(\frac{5}{338}\right) e(3239)e\left(\frac{32}{39}\right)
χ8788(19,⋅)\chi_{8788}(19,\cdot) 8788.w 156 no 11 11 e(3178)e\left(\frac{31}{78}\right) e(4752)e\left(\frac{47}{52}\right) e(73156)e\left(\frac{73}{156}\right) e(3139)e\left(\frac{31}{39}\right) e(149156)e\left(\frac{149}{156}\right) e(47156)e\left(\frac{47}{156}\right) e(1778)e\left(\frac{17}{78}\right) e(712)e\left(\frac{7}{12}\right) e(4552)e\left(\frac{45}{52}\right) e(23)e\left(\frac{2}{3}\right)
χ8788(21,⋅)\chi_{8788}(21,\cdot) 8788.be 676 no −1-1 11 e(34169)e\left(\frac{34}{169}\right) e(69676)e\left(\frac{69}{676}\right) e(647676)e\left(\frac{647}{676}\right) e(68169)e\left(\frac{68}{169}\right) e(391676)e\left(\frac{391}{676}\right) e(205676)e\left(\frac{205}{676}\right) e(5338)e\left(\frac{5}{338}\right) e(4552)e\left(\frac{45}{52}\right) e(107676)e\left(\frac{107}{676}\right) e(926)e\left(\frac{9}{26}\right)
χ8788(23,⋅)\chi_{8788}(23,\cdot) 8788.u 78 no −1-1 11 e(4178)e\left(\frac{41}{78}\right) e(2526)e\left(\frac{25}{26}\right) e(3239)e\left(\frac{32}{39}\right) e(239)e\left(\frac{2}{39}\right) e(3739)e\left(\frac{37}{39}\right) e(1939)e\left(\frac{19}{39}\right) e(3239)e\left(\frac{32}{39}\right) e(23)e\left(\frac{2}{3}\right) e(926)e\left(\frac{9}{26}\right) e(56)e\left(\frac{5}{6}\right)
χ8788(25,⋅)\chi_{8788}(25,\cdot) 8788.ba 338 no 11 11 e(17169)e\left(\frac{17}{169}\right) e(313338)e\left(\frac{313}{338}\right) e(35338)e\left(\frac{35}{338}\right) e(34169)e\left(\frac{34}{169}\right) e(309338)e\left(\frac{309}{338}\right) e(9338)e\left(\frac{9}{338}\right) e(128169)e\left(\frac{128}{169}\right) e(2126)e\left(\frac{21}{26}\right) e(69338)e\left(\frac{69}{338}\right) e(1213)e\left(\frac{12}{13}\right)
χ8788(27,⋅)\chi_{8788}(27,\cdot) 8788.bb 338 yes −1-1 11 e(5338)e\left(\frac{5}{338}\right) e(110169)e\left(\frac{110}{169}\right) e(199338)e\left(\frac{199}{338}\right) e(5169)e\left(\frac{5}{169}\right) e(289338)e\left(\frac{289}{338}\right) e(225338)e\left(\frac{225}{338}\right) e(158169)e\left(\frac{158}{169}\right) e(526)e\left(\frac{5}{26}\right) e(102169)e\left(\frac{102}{169}\right) e(1526)e\left(\frac{15}{26}\right)
χ8788(29,⋅)\chi_{8788}(29,\cdot) 8788.bc 507 no 11 11 e(421507)e\left(\frac{421}{507}\right) e(147169)e\left(\frac{147}{169}\right) e(329507)e\left(\frac{329}{507}\right) e(335507)e\left(\frac{335}{507}\right) e(133507)e\left(\frac{133}{507}\right) e(355507)e\left(\frac{355}{507}\right) e(446507)e\left(\frac{446}{507}\right) e(539)e\left(\frac{5}{39}\right) e(81169)e\left(\frac{81}{169}\right) e(2839)e\left(\frac{28}{39}\right)
χ8788(31,⋅)\chi_{8788}(31,\cdot) 8788.bd 676 yes 11 11 e(265338)e\left(\frac{265}{338}\right) e(167676)e\left(\frac{167}{676}\right) e(307676)e\left(\frac{307}{676}\right) e(96169)e\left(\frac{96}{169}\right) e(383676)e\left(\frac{383}{676}\right) e(21676)e\left(\frac{21}{676}\right) e(17338)e\left(\frac{17}{338}\right) e(4952)e\left(\frac{49}{52}\right) e(161676)e\left(\frac{161}{676}\right) e(113)e\left(\frac{1}{13}\right)
χ8788(33,⋅)\chi_{8788}(33,\cdot) 8788.bi 2028 no −1-1 11 e(485507)e\left(\frac{485}{507}\right) e(5676)e\left(\frac{5}{676}\right) e(16692028)e\left(\frac{1669}{2028}\right) e(463507)e\left(\frac{463}{507}\right) e(7612028)e\left(\frac{761}{2028}\right) e(19552028)e\left(\frac{1955}{2028}\right) e(9711014)e\left(\frac{971}{1014}\right) e(55156)e\left(\frac{55}{156}\right) e(527676)e\left(\frac{527}{676}\right) e(3778)e\left(\frac{37}{78}\right)
χ8788(35,⋅)\chi_{8788}(35,\cdot) 8788.bf 1014 yes −1-1 11 e(7571014)e\left(\frac{757}{1014}\right) e(87169)e\left(\frac{87}{169}\right) e(3171014)e\left(\frac{317}{1014}\right) e(250507)e\left(\frac{250}{507}\right) e(851014)e\left(\frac{85}{1014}\right) e(2651014)e\left(\frac{265}{1014}\right) e(295507)e\left(\frac{295}{507}\right) e(2978)e\left(\frac{29}{78}\right) e(10169)e\left(\frac{10}{169}\right) e(6178)e\left(\frac{61}{78}\right)
χ8788(37,⋅)\chi_{8788}(37,\cdot) 8788.bi 2028 no −1-1 11 e(1507)e\left(\frac{1}{507}\right) e(453676)e\left(\frac{453}{676}\right) e(8692028)e\left(\frac{869}{2028}\right) e(2507)e\left(\frac{2}{507}\right) e(2652028)e\left(\frac{265}{2028}\right) e(13632028)e\left(\frac{1363}{2028}\right) e(251014)e\left(\frac{25}{1014}\right) e(95156)e\left(\frac{95}{156}\right) e(291676)e\left(\frac{291}{676}\right) e(7178)e\left(\frac{71}{78}\right)
χ8788(41,⋅)\chi_{8788}(41,\cdot) 8788.bi 2028 no −1-1 11 e(412507)e\left(\frac{412}{507}\right) e(567676)e\left(\frac{567}{676}\right) e(16072028)e\left(\frac{1607}{2028}\right) e(317507)e\left(\frac{317}{507}\right) e(1752028)e\left(\frac{175}{2028}\right) e(13212028)e\left(\frac{1321}{2028}\right) e(6671014)e\left(\frac{667}{1014}\right) e(101156)e\left(\frac{101}{156}\right) e(409676)e\left(\frac{409}{676}\right) e(4178)e\left(\frac{41}{78}\right)
χ8788(43,⋅)\chi_{8788}(43,\cdot) 8788.bh 1014 yes −1-1 11 e(6611014)e\left(\frac{661}{1014}\right) e(287338)e\left(\frac{287}{338}\right) e(124507)e\left(\frac{124}{507}\right) e(154507)e\left(\frac{154}{507}\right) e(158507)e\left(\frac{158}{507}\right) e(254507)e\left(\frac{254}{507}\right) e(202507)e\left(\frac{202}{507}\right) e(2539)e\left(\frac{25}{39}\right) e(303338)e\left(\frac{303}{338}\right) e(778)e\left(\frac{7}{78}\right)
χ8788(45,⋅)\chi_{8788}(45,\cdot) 8788.bi 2028 no −1-1 11 e(284507)e\left(\frac{284}{507}\right) e(43676)e\left(\frac{43}{676}\right) e(19152028)e\left(\frac{1915}{2028}\right) e(61507)e\left(\frac{61}{507}\right) e(7312028)e\left(\frac{731}{2028}\right) e(12652028)e\left(\frac{1265}{2028}\right) e(5091014)e\left(\frac{509}{1014}\right) e(109156)e\left(\frac{109}{156}\right) e(341676)e\left(\frac{341}{676}\right) e(178)e\left(\frac{1}{78}\right)
χ8788(47,⋅)\chi_{8788}(47,\cdot) 8788.bd 676 yes 11 11 e(249338)e\left(\frac{249}{338}\right) e(449676)e\left(\frac{449}{676}\right) e(453676)e\left(\frac{453}{676}\right) e(80169)e\left(\frac{80}{169}\right) e(629676)e\left(\frac{629}{676}\right) e(271676)e\left(\frac{271}{676}\right) e(155338)e\left(\frac{155}{338}\right) e(4352)e\left(\frac{43}{52}\right) e(275676)e\left(\frac{275}{676}\right) e(313)e\left(\frac{3}{13}\right)
χ8788(49,⋅)\chi_{8788}(49,\cdot) 8788.bg 1014 no 11 11 e(199507)e\left(\frac{199}{507}\right) e(35338)e\left(\frac{35}{338}\right) e(5291014)e\left(\frac{529}{1014}\right) e(398507)e\left(\frac{398}{507}\right) e(2571014)e\left(\frac{257}{1014}\right) e(5031014)e\left(\frac{503}{1014}\right) e(206507)e\left(\frac{206}{507}\right) e(7378)e\left(\frac{73}{78}\right) e(309338)e\left(\frac{309}{338}\right) e(2539)e\left(\frac{25}{39}\right)
χ8788(51,⋅)\chi_{8788}(51,\cdot) 8788.z 338 yes −1-1 11 e(107338)e\left(\frac{107}{338}\right) e(145338)e\left(\frac{145}{338}\right) e(152169)e\left(\frac{152}{169}\right) e(107169)e\left(\frac{107}{169}\right) e(101169)e\left(\frac{101}{169}\right) e(126169)e\left(\frac{126}{169}\right) e(35169)e\left(\frac{35}{169}\right) e(813)e\left(\frac{8}{13}\right) e(73338)e\left(\frac{73}{338}\right) e(926)e\left(\frac{9}{26}\right)
χ8788(53,⋅)\chi_{8788}(53,\cdot) 8788.y 169 no 11 11 e(109169)e\left(\frac{109}{169}\right) e(64169)e\left(\frac{64}{169}\right) e(147169)e\left(\frac{147}{169}\right) e(49169)e\left(\frac{49}{169}\right) e(81169)e\left(\frac{81}{169}\right) e(4169)e\left(\frac{4}{169}\right) e(95169)e\left(\frac{95}{169}\right) e(513)e\left(\frac{5}{13}\right) e(87169)e\left(\frac{87}{169}\right) e(213)e\left(\frac{2}{13}\right)
χ8788(55,⋅)\chi_{8788}(55,\cdot) 8788.bf 1014 yes −1-1 11 e(5091014)e\left(\frac{509}{1014}\right) e(71169)e\left(\frac{71}{169}\right) e(1811014)e\left(\frac{181}{1014}\right) e(2507)e\left(\frac{2}{507}\right) e(8931014)e\left(\frac{893}{1014}\right) e(9351014)e\left(\frac{935}{1014}\right) e(266507)e\left(\frac{266}{507}\right) e(6778)e\left(\frac{67}{78}\right) e(115169)e\left(\frac{115}{169}\right) e(7178)e\left(\frac{71}{78}\right)
χ8788(57,⋅)\chi_{8788}(57,\cdot) 8788.be 676 no −1-1 11 e(68169)e\left(\frac{68}{169}\right) e(307676)e\left(\frac{307}{676}\right) e(449676)e\left(\frac{449}{676}\right) e(136169)e\left(\frac{136}{169}\right) e(613676)e\left(\frac{613}{676}\right) e(579676)e\left(\frac{579}{676}\right) e(179338)e\left(\frac{179}{338}\right) e(5152)e\left(\frac{51}{52}\right) e(45676)e\left(\frac{45}{676}\right) e(526)e\left(\frac{5}{26}\right)
χ8788(59,⋅)\chi_{8788}(59,\cdot) 8788.bj 2028 yes 11 11 e(1811014)e\left(\frac{181}{1014}\right) e(521676)e\left(\frac{521}{676}\right) e(13272028)e\left(\frac{1327}{2028}\right) e(181507)e\left(\frac{181}{507}\right) e(4072028)e\left(\frac{407}{2028}\right) e(19252028)e\left(\frac{1925}{2028}\right) e(9951014)e\left(\frac{995}{1014}\right) e(37156)e\left(\frac{37}{156}\right) e(563676)e\left(\frac{563}{676}\right) e(539)e\left(\frac{5}{39}\right)
χ8788(61,⋅)\chi_{8788}(61,\cdot) 8788.bc 507 no 11 11 e(11507)e\left(\frac{11}{507}\right) e(105169)e\left(\frac{105}{169}\right) e(235507)e\left(\frac{235}{507}\right) e(22507)e\left(\frac{22}{507}\right) e(95507)e\left(\frac{95}{507}\right) e(326507)e\left(\frac{326}{507}\right) e(391507)e\left(\frac{391}{507}\right) e(3739)e\left(\frac{37}{39}\right) e(82169)e\left(\frac{82}{169}\right) e(2039)e\left(\frac{20}{39}\right)
χ8788(63,⋅)\chi_{8788}(63,\cdot) 8788.bj 2028 yes 11 11 e(2091014)e\left(\frac{209}{1014}\right) e(441676)e\left(\frac{441}{676}\right) e(3112028)e\left(\frac{311}{2028}\right) e(209507)e\left(\frac{209}{507}\right) e(10752028)e\left(\frac{1075}{2028}\right) e(17412028)e\left(\frac{1741}{2028}\right) e(3311014)e\left(\frac{331}{1014}\right) e(41156)e\left(\frac{41}{156}\right) e(243676)e\left(\frac{243}{676}\right) e(3439)e\left(\frac{34}{39}\right)
χ8788(67,⋅)\chi_{8788}(67,\cdot) 8788.bj 2028 yes 11 11 e(2271014)e\left(\frac{227}{1014}\right) e(631676)e\left(\frac{631}{676}\right) e(15412028)e\left(\frac{1541}{2028}\right) e(227507)e\left(\frac{227}{507}\right) e(9252028)e\left(\frac{925}{2028}\right) e(3192028)e\left(\frac{319}{2028}\right) e(491014)e\left(\frac{49}{1014}\right) e(155156)e\left(\frac{155}{156}\right) e(665676)e\left(\frac{665}{676}\right) e(2239)e\left(\frac{22}{39}\right)
χ8788(69,⋅)\chi_{8788}(69,\cdot) 8788.bg 1014 no 11 11 e(269507)e\left(\frac{269}{507}\right) e(173338)e\left(\frac{173}{338}\right) e(171014)e\left(\frac{17}{1014}\right) e(31507)e\left(\frac{31}{507}\right) e(9131014)e\left(\frac{913}{1014}\right) e(431014)e\left(\frac{43}{1014}\right) e(67507)e\left(\frac{67}{507}\right) e(578)e\left(\frac{5}{78}\right) e(185338)e\left(\frac{185}{338}\right) e(1439)e\left(\frac{14}{39}\right)
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