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Properties

Modulus 80488048
Structure C2×C2×C1004C_{2}\times C_{2}\times C_{1004}
Order 40164016

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(8048)
 
pari: g = idealstar(,8048,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4016
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C1004C_{2}\times C_{2}\times C_{1004}
sage: H.gens()
 
pari: g.gen
 
Generators = χ8048(1007,⋅)\chi_{8048}(1007,\cdot), χ8048(6037,⋅)\chi_{8048}(6037,\cdot), χ8048(2017,⋅)\chi_{8048}(2017,\cdot)

First 32 of 4016 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 1313 1515 1717 1919 2121
χ8048(1,⋅)\chi_{8048}(1,\cdot) 8048.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ8048(3,⋅)\chi_{8048}(3,\cdot) 8048.v 1004 yes −1-1 11 e(2291004)e\left(\frac{229}{1004}\right) e(611004)e\left(\frac{61}{1004}\right) e(182251)e\left(\frac{182}{251}\right) e(229502)e\left(\frac{229}{502}\right) e(3031004)e\left(\frac{303}{1004}\right) e(7871004)e\left(\frac{787}{1004}\right) e(145502)e\left(\frac{145}{502}\right) e(41251)e\left(\frac{41}{251}\right) e(4011004)e\left(\frac{401}{1004}\right) e(9571004)e\left(\frac{957}{1004}\right)
χ8048(5,⋅)\chi_{8048}(5,\cdot) 8048.x 1004 yes −1-1 11 e(611004)e\left(\frac{61}{1004}\right) e(2531004)e\left(\frac{253}{1004}\right) e(337502)e\left(\frac{337}{502}\right) e(61502)e\left(\frac{61}{502}\right) e(3351004)e\left(\frac{335}{1004}\right) e(10011004)e\left(\frac{1001}{1004}\right) e(157502)e\left(\frac{157}{502}\right) e(229502)e\left(\frac{229}{502}\right) e(2231004)e\left(\frac{223}{1004}\right) e(7351004)e\left(\frac{735}{1004}\right)
χ8048(7,⋅)\chi_{8048}(7,\cdot) 8048.p 502 no −1-1 11 e(182251)e\left(\frac{182}{251}\right) e(337502)e\left(\frac{337}{502}\right) e(117502)e\left(\frac{117}{502}\right) e(113251)e\left(\frac{113}{251}\right) e(49251)e\left(\frac{49}{251}\right) e(373502)e\left(\frac{373}{502}\right) e(199502)e\left(\frac{199}{502}\right) e(58251)e\left(\frac{58}{251}\right) e(151251)e\left(\frac{151}{251}\right) e(481502)e\left(\frac{481}{502}\right)
χ8048(9,⋅)\chi_{8048}(9,\cdot) 8048.s 502 no 11 11 e(229502)e\left(\frac{229}{502}\right) e(61502)e\left(\frac{61}{502}\right) e(113251)e\left(\frac{113}{251}\right) e(229251)e\left(\frac{229}{251}\right) e(303502)e\left(\frac{303}{502}\right) e(285502)e\left(\frac{285}{502}\right) e(145251)e\left(\frac{145}{251}\right) e(82251)e\left(\frac{82}{251}\right) e(401502)e\left(\frac{401}{502}\right) e(455502)e\left(\frac{455}{502}\right)
χ8048(11,⋅)\chi_{8048}(11,\cdot) 8048.v 1004 yes −1-1 11 e(3031004)e\left(\frac{303}{1004}\right) e(3351004)e\left(\frac{335}{1004}\right) e(49251)e\left(\frac{49}{251}\right) e(303502)e\left(\frac{303}{502}\right) e(2651004)e\left(\frac{265}{1004}\right) e(1251004)e\left(\frac{125}{1004}\right) e(319502)e\left(\frac{319}{502}\right) e(40251)e\left(\frac{40}{251}\right) e(791004)e\left(\frac{79}{1004}\right) e(4991004)e\left(\frac{499}{1004}\right)
χ8048(13,⋅)\chi_{8048}(13,\cdot) 8048.w 1004 yes 11 11 e(7871004)e\left(\frac{787}{1004}\right) e(10011004)e\left(\frac{1001}{1004}\right) e(373502)e\left(\frac{373}{502}\right) e(285502)e\left(\frac{285}{502}\right) e(1251004)e\left(\frac{125}{1004}\right) e(8831004)e\left(\frac{883}{1004}\right) e(196251)e\left(\frac{196}{251}\right) e(142251)e\left(\frac{142}{251}\right) e(7951004)e\left(\frac{795}{1004}\right) e(5291004)e\left(\frac{529}{1004}\right)
χ8048(15,⋅)\chi_{8048}(15,\cdot) 8048.t 502 no 11 11 e(145502)e\left(\frac{145}{502}\right) e(157502)e\left(\frac{157}{502}\right) e(199502)e\left(\frac{199}{502}\right) e(145251)e\left(\frac{145}{251}\right) e(319502)e\left(\frac{319}{502}\right) e(196251)e\left(\frac{196}{251}\right) e(151251)e\left(\frac{151}{251}\right) e(311502)e\left(\frac{311}{502}\right) e(156251)e\left(\frac{156}{251}\right) e(172251)e\left(\frac{172}{251}\right)
χ8048(17,⋅)\chi_{8048}(17,\cdot) 8048.o 502 no −1-1 11 e(41251)e\left(\frac{41}{251}\right) e(229502)e\left(\frac{229}{502}\right) e(58251)e\left(\frac{58}{251}\right) e(82251)e\left(\frac{82}{251}\right) e(40251)e\left(\frac{40}{251}\right) e(142251)e\left(\frac{142}{251}\right) e(311502)e\left(\frac{311}{502}\right) e(233502)e\left(\frac{233}{502}\right) e(57502)e\left(\frac{57}{502}\right) e(99251)e\left(\frac{99}{251}\right)
χ8048(19,⋅)\chi_{8048}(19,\cdot) 8048.u 1004 yes 11 11 e(4011004)e\left(\frac{401}{1004}\right) e(2231004)e\left(\frac{223}{1004}\right) e(151251)e\left(\frac{151}{251}\right) e(401502)e\left(\frac{401}{502}\right) e(791004)e\left(\frac{79}{1004}\right) e(7951004)e\left(\frac{795}{1004}\right) e(156251)e\left(\frac{156}{251}\right) e(57502)e\left(\frac{57}{502}\right) e(6431004)e\left(\frac{643}{1004}\right) e(11004)e\left(\frac{1}{1004}\right)
χ8048(21,⋅)\chi_{8048}(21,\cdot) 8048.w 1004 yes 11 11 e(9571004)e\left(\frac{957}{1004}\right) e(7351004)e\left(\frac{735}{1004}\right) e(481502)e\left(\frac{481}{502}\right) e(455502)e\left(\frac{455}{502}\right) e(4991004)e\left(\frac{499}{1004}\right) e(5291004)e\left(\frac{529}{1004}\right) e(172251)e\left(\frac{172}{251}\right) e(99251)e\left(\frac{99}{251}\right) e(11004)e\left(\frac{1}{1004}\right) e(9151004)e\left(\frac{915}{1004}\right)
χ8048(23,⋅)\chi_{8048}(23,\cdot) 8048.p 502 no −1-1 11 e(164251)e\left(\frac{164}{251}\right) e(163502)e\left(\frac{163}{502}\right) e(213502)e\left(\frac{213}{502}\right) e(77251)e\left(\frac{77}{251}\right) e(160251)e\left(\frac{160}{251}\right) e(383502)e\left(\frac{383}{502}\right) e(491502)e\left(\frac{491}{502}\right) e(215251)e\left(\frac{215}{251}\right) e(114251)e\left(\frac{114}{251}\right) e(39502)e\left(\frac{39}{502}\right)
χ8048(25,⋅)\chi_{8048}(25,\cdot) 8048.s 502 no 11 11 e(61502)e\left(\frac{61}{502}\right) e(253502)e\left(\frac{253}{502}\right) e(86251)e\left(\frac{86}{251}\right) e(61251)e\left(\frac{61}{251}\right) e(335502)e\left(\frac{335}{502}\right) e(499502)e\left(\frac{499}{502}\right) e(157251)e\left(\frac{157}{251}\right) e(229251)e\left(\frac{229}{251}\right) e(223502)e\left(\frac{223}{502}\right) e(233502)e\left(\frac{233}{502}\right)
χ8048(27,⋅)\chi_{8048}(27,\cdot) 8048.v 1004 yes −1-1 11 e(6871004)e\left(\frac{687}{1004}\right) e(1831004)e\left(\frac{183}{1004}\right) e(44251)e\left(\frac{44}{251}\right) e(185502)e\left(\frac{185}{502}\right) e(9091004)e\left(\frac{909}{1004}\right) e(3531004)e\left(\frac{353}{1004}\right) e(435502)e\left(\frac{435}{502}\right) e(123251)e\left(\frac{123}{251}\right) e(1991004)e\left(\frac{199}{1004}\right) e(8631004)e\left(\frac{863}{1004}\right)
χ8048(29,⋅)\chi_{8048}(29,\cdot) 8048.x 1004 yes −1-1 11 e(1711004)e\left(\frac{171}{1004}\right) e(1991004)e\left(\frac{199}{1004}\right) e(23502)e\left(\frac{23}{502}\right) e(171502)e\left(\frac{171}{502}\right) e(5771004)e\left(\frac{577}{1004}\right) e(8311004)e\left(\frac{831}{1004}\right) e(185502)e\left(\frac{185}{502}\right) e(321502)e\left(\frac{321}{502}\right) e(4771004)e\left(\frac{477}{1004}\right) e(2171004)e\left(\frac{217}{1004}\right)
χ8048(31,⋅)\chi_{8048}(31,\cdot) 8048.t 502 no 11 11 e(67502)e\left(\frac{67}{502}\right) e(31502)e\left(\frac{31}{502}\right) e(407502)e\left(\frac{407}{502}\right) e(67251)e\left(\frac{67}{251}\right) e(47502)e\left(\frac{47}{502}\right) e(165251)e\left(\frac{165}{251}\right) e(49251)e\left(\frac{49}{251}\right) e(71502)e\left(\frac{71}{502}\right) e(34251)e\left(\frac{34}{251}\right) e(237251)e\left(\frac{237}{251}\right)
χ8048(33,⋅)\chi_{8048}(33,\cdot) 8048.m 251 no 11 11 e(133251)e\left(\frac{133}{251}\right) e(99251)e\left(\frac{99}{251}\right) e(231251)e\left(\frac{231}{251}\right) e(15251)e\left(\frac{15}{251}\right) e(142251)e\left(\frac{142}{251}\right) e(228251)e\left(\frac{228}{251}\right) e(232251)e\left(\frac{232}{251}\right) e(81251)e\left(\frac{81}{251}\right) e(120251)e\left(\frac{120}{251}\right) e(113251)e\left(\frac{113}{251}\right)
χ8048(35,⋅)\chi_{8048}(35,\cdot) 8048.u 1004 yes 11 11 e(7891004)e\left(\frac{789}{1004}\right) e(9271004)e\left(\frac{927}{1004}\right) e(227251)e\left(\frac{227}{251}\right) e(287502)e\left(\frac{287}{502}\right) e(5311004)e\left(\frac{531}{1004}\right) e(7431004)e\left(\frac{743}{1004}\right) e(178251)e\left(\frac{178}{251}\right) e(345502)e\left(\frac{345}{502}\right) e(8271004)e\left(\frac{827}{1004}\right) e(6931004)e\left(\frac{693}{1004}\right)
χ8048(37,⋅)\chi_{8048}(37,\cdot) 8048.x 1004 yes −1-1 11 e(411004)e\left(\frac{41}{1004}\right) e(9931004)e\left(\frac{993}{1004}\right) e(29502)e\left(\frac{29}{502}\right) e(41502)e\left(\frac{41}{502}\right) e(2911004)e\left(\frac{291}{1004}\right) e(3931004)e\left(\frac{393}{1004}\right) e(15502)e\left(\frac{15}{502}\right) e(121502)e\left(\frac{121}{502}\right) e(9071004)e\left(\frac{907}{1004}\right) e(991004)e\left(\frac{99}{1004}\right)
χ8048(39,⋅)\chi_{8048}(39,\cdot) 8048.p 502 no −1-1 11 e(3251)e\left(\frac{3}{251}\right) e(29502)e\left(\frac{29}{502}\right) e(235502)e\left(\frac{235}{502}\right) e(6251)e\left(\frac{6}{251}\right) e(107251)e\left(\frac{107}{251}\right) e(333502)e\left(\frac{333}{502}\right) e(35502)e\left(\frac{35}{502}\right) e(183251)e\left(\frac{183}{251}\right) e(48251)e\left(\frac{48}{251}\right) e(241502)e\left(\frac{241}{502}\right)
χ8048(41,⋅)\chi_{8048}(41,\cdot) 8048.q 502 no −1-1 11 e(265502)e\left(\frac{265}{502}\right) e(243251)e\left(\frac{243}{251}\right) e(65251)e\left(\frac{65}{251}\right) e(14251)e\left(\frac{14}{251}\right) e(81502)e\left(\frac{81}{502}\right) e(275502)e\left(\frac{275}{502}\right) e(249502)e\left(\frac{249}{502}\right) e(101502)e\left(\frac{101}{502}\right) e(112251)e\left(\frac{112}{251}\right) e(395502)e\left(\frac{395}{502}\right)
χ8048(43,⋅)\chi_{8048}(43,\cdot) 8048.v 1004 yes −1-1 11 e(7631004)e\left(\frac{763}{1004}\right) e(3831004)e\left(\frac{383}{1004}\right) e(77251)e\left(\frac{77}{251}\right) e(261502)e\left(\frac{261}{502}\right) e(2731004)e\left(\frac{273}{1004}\right) e(531004)e\left(\frac{53}{1004}\right) e(71502)e\left(\frac{71}{502}\right) e(27251)e\left(\frac{27}{251}\right) e(4111004)e\left(\frac{411}{1004}\right) e(671004)e\left(\frac{67}{1004}\right)
χ8048(45,⋅)\chi_{8048}(45,\cdot) 8048.x 1004 yes −1-1 11 e(5191004)e\left(\frac{519}{1004}\right) e(3751004)e\left(\frac{375}{1004}\right) e(61502)e\left(\frac{61}{502}\right) e(17502)e\left(\frac{17}{502}\right) e(9411004)e\left(\frac{941}{1004}\right) e(5671004)e\left(\frac{567}{1004}\right) e(447502)e\left(\frac{447}{502}\right) e(393502)e\left(\frac{393}{502}\right) e(211004)e\left(\frac{21}{1004}\right) e(6411004)e\left(\frac{641}{1004}\right)
χ8048(47,⋅)\chi_{8048}(47,\cdot) 8048.r 502 no −1-1 11 e(475502)e\left(\frac{475}{502}\right) e(123251)e\left(\frac{123}{251}\right) e(323502)e\left(\frac{323}{502}\right) e(224251)e\left(\frac{224}{251}\right) e(41502)e\left(\frac{41}{502}\right) e(192251)e\left(\frac{192}{251}\right) e(219502)e\left(\frac{219}{502}\right) e(55251)e\left(\frac{55}{251}\right) e(321502)e\left(\frac{321}{502}\right) e(148251)e\left(\frac{148}{251}\right)
χ8048(49,⋅)\chi_{8048}(49,\cdot) 8048.m 251 no 11 11 e(113251)e\left(\frac{113}{251}\right) e(86251)e\left(\frac{86}{251}\right) e(117251)e\left(\frac{117}{251}\right) e(226251)e\left(\frac{226}{251}\right) e(98251)e\left(\frac{98}{251}\right) e(122251)e\left(\frac{122}{251}\right) e(199251)e\left(\frac{199}{251}\right) e(116251)e\left(\frac{116}{251}\right) e(51251)e\left(\frac{51}{251}\right) e(230251)e\left(\frac{230}{251}\right)
χ8048(51,⋅)\chi_{8048}(51,\cdot) 8048.u 1004 yes 11 11 e(3931004)e\left(\frac{393}{1004}\right) e(5191004)e\left(\frac{519}{1004}\right) e(240251)e\left(\frac{240}{251}\right) e(393502)e\left(\frac{393}{502}\right) e(4631004)e\left(\frac{463}{1004}\right) e(3511004)e\left(\frac{351}{1004}\right) e(228251)e\left(\frac{228}{251}\right) e(315502)e\left(\frac{315}{502}\right) e(5151004)e\left(\frac{515}{1004}\right) e(3491004)e\left(\frac{349}{1004}\right)
χ8048(53,⋅)\chi_{8048}(53,\cdot) 8048.x 1004 yes −1-1 11 e(1011004)e\left(\frac{101}{1004}\right) e(7811004)e\left(\frac{781}{1004}\right) e(451502)e\left(\frac{451}{502}\right) e(101502)e\left(\frac{101}{502}\right) e(4231004)e\left(\frac{423}{1004}\right) e(2091004)e\left(\frac{209}{1004}\right) e(441502)e\left(\frac{441}{502}\right) e(445502)e\left(\frac{445}{502}\right) e(8631004)e\left(\frac{863}{1004}\right) e(10031004)e\left(\frac{1003}{1004}\right)
χ8048(55,⋅)\chi_{8048}(55,\cdot) 8048.n 502 no 11 11 e(91251)e\left(\frac{91}{251}\right) e(147251)e\left(\frac{147}{251}\right) e(435502)e\left(\frac{435}{502}\right) e(182251)e\left(\frac{182}{251}\right) e(150251)e\left(\frac{150}{251}\right) e(61502)e\left(\frac{61}{502}\right) e(238251)e\left(\frac{238}{251}\right) e(309502)e\left(\frac{309}{502}\right) e(151502)e\left(\frac{151}{502}\right) e(115502)e\left(\frac{115}{502}\right)
χ8048(57,⋅)\chi_{8048}(57,\cdot) 8048.q 502 no −1-1 11 e(315502)e\left(\frac{315}{502}\right) e(71251)e\left(\frac{71}{251}\right) e(82251)e\left(\frac{82}{251}\right) e(64251)e\left(\frac{64}{251}\right) e(191502)e\left(\frac{191}{502}\right) e(289502)e\left(\frac{289}{502}\right) e(457502)e\left(\frac{457}{502}\right) e(139502)e\left(\frac{139}{502}\right) e(10251)e\left(\frac{10}{251}\right) e(479502)e\left(\frac{479}{502}\right)
χ8048(59,⋅)\chi_{8048}(59,\cdot) 8048.v 1004 yes −1-1 11 e(5671004)e\left(\frac{567}{1004}\right) e(6071004)e\left(\frac{607}{1004}\right) e(124251)e\left(\frac{124}{251}\right) e(65502)e\left(\frac{65}{502}\right) e(6451004)e\left(\frac{645}{1004}\right) e(7211004)e\left(\frac{721}{1004}\right) e(85502)e\left(\frac{85}{502}\right) e(50251)e\left(\frac{50}{251}\right) e(2871004)e\left(\frac{287}{1004}\right) e(591004)e\left(\frac{59}{1004}\right)
χ8048(61,⋅)\chi_{8048}(61,\cdot) 8048.w 1004 yes 11 11 e(7231004)e\left(\frac{723}{1004}\right) e(3571004)e\left(\frac{357}{1004}\right) e(291502)e\left(\frac{291}{502}\right) e(221502)e\left(\frac{221}{502}\right) e(1851004)e\left(\frac{185}{1004}\right) e(3431004)e\left(\frac{343}{1004}\right) e(19251)e\left(\frac{19}{251}\right) e(170251)e\left(\frac{170}{251}\right) e(7751004)e\left(\frac{775}{1004}\right) e(3011004)e\left(\frac{301}{1004}\right)
χ8048(63,⋅)\chi_{8048}(63,\cdot) 8048.r 502 no −1-1 11 e(91502)e\left(\frac{91}{502}\right) e(199251)e\left(\frac{199}{251}\right) e(343502)e\left(\frac{343}{502}\right) e(91251)e\left(\frac{91}{251}\right) e(401502)e\left(\frac{401}{502}\right) e(78251)e\left(\frac{78}{251}\right) e(489502)e\left(\frac{489}{502}\right) e(140251)e\left(\frac{140}{251}\right) e(201502)e\left(\frac{201}{502}\right) e(217251)e\left(\frac{217}{251}\right)
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