Properties

Modulus 216000216000
Structure C2×C2×C4×C3600C_{2}\times C_{2}\times C_{4}\times C_{3600}
Order 5760057600

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(216000)
 
pari: g = idealstar(,216000,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 57600
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C4×C3600C_{2}\times C_{2}\times C_{4}\times C_{3600}
sage: H.gens()
 
pari: g.gen
 
Generators = χ216000(114751,)\chi_{216000}(114751,\cdot), χ216000(202501,)\chi_{216000}(202501,\cdot), χ216000(136001,)\chi_{216000}(136001,\cdot), χ216000(29377,)\chi_{216000}(29377,\cdot)

First 32 of 57600 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 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ216000(1,)\chi_{216000}(1,\cdot) 216000.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ216000(7,)\chi_{216000}(7,\cdot) 216000.th 360 no 11 11 e(29)e\left(\frac{2}{9}\right) e(281360)e\left(\frac{281}{360}\right) e(229360)e\left(\frac{229}{360}\right) e(5360)e\left(\frac{53}{60}\right) e(101120)e\left(\frac{101}{120}\right) e(1745)e\left(\frac{17}{45}\right) e(167360)e\left(\frac{167}{360}\right) e(790)e\left(\frac{7}{90}\right) e(73120)e\left(\frac{73}{120}\right) e(47180)e\left(\frac{47}{180}\right)
χ216000(11,)\chi_{216000}(11,\cdot) 216000.yp 3600 yes 11 11 e(281360)e\left(\frac{281}{360}\right) e(7613600)e\left(\frac{761}{3600}\right) e(3793600)e\left(\frac{379}{3600}\right) e(19300)e\left(\frac{19}{300}\right) e(411200)e\left(\frac{41}{1200}\right) e(6831800)e\left(\frac{683}{1800}\right) e(10073600)e\left(\frac{1007}{3600}\right) e(208225)e\left(\frac{208}{225}\right) e(2231200)e\left(\frac{223}{1200}\right) e(1671800)e\left(\frac{167}{1800}\right)
χ216000(13,)\chi_{216000}(13,\cdot) 216000.yv 3600 yes 1-1 11 e(229360)e\left(\frac{229}{360}\right) e(3793600)e\left(\frac{379}{3600}\right) e(29813600)e\left(\frac{2981}{3600}\right) e(2975)e\left(\frac{29}{75}\right) e(10991200)e\left(\frac{1099}{1200}\right) e(1871800)e\left(\frac{187}{1800}\right) e(33733600)e\left(\frac{3373}{3600}\right) e(49450)e\left(\frac{49}{450}\right) e(4971200)e\left(\frac{497}{1200}\right) e(15131800)e\left(\frac{1513}{1800}\right)
χ216000(17,)\chi_{216000}(17,\cdot) 216000.sl 300 no 11 11 e(5360)e\left(\frac{53}{60}\right) e(19300)e\left(\frac{19}{300}\right) e(2975)e\left(\frac{29}{75}\right) e(79100)e\left(\frac{79}{100}\right) e(39100)e\left(\frac{39}{100}\right) e(89300)e\left(\frac{89}{300}\right) e(103300)e\left(\frac{103}{300}\right) e(5375)e\left(\frac{53}{75}\right) e(2325)e\left(\frac{23}{25}\right) e(5975)e\left(\frac{59}{75}\right)
χ216000(19,)\chi_{216000}(19,\cdot) 216000.xk 1200 no 1-1 11 e(101120)e\left(\frac{101}{120}\right) e(411200)e\left(\frac{41}{1200}\right) e(10991200)e\left(\frac{1099}{1200}\right) e(39100)e\left(\frac{39}{100}\right) e(321400)e\left(\frac{321}{400}\right) e(323600)e\left(\frac{323}{600}\right) e(7671200)e\left(\frac{767}{1200}\right) e(7375)e\left(\frac{73}{75}\right) e(63400)e\left(\frac{63}{400}\right) e(227600)e\left(\frac{227}{600}\right)
χ216000(23,)\chi_{216000}(23,\cdot) 216000.yd 1800 no 1-1 11 e(1745)e\left(\frac{17}{45}\right) e(6831800)e\left(\frac{683}{1800}\right) e(1871800)e\left(\frac{187}{1800}\right) e(89300)e\left(\frac{89}{300}\right) e(323600)e\left(\frac{323}{600}\right) e(37450)e\left(\frac{37}{450}\right) e(8211800)e\left(\frac{821}{1800}\right) e(271450)e\left(\frac{271}{450}\right) e(319600)e\left(\frac{319}{600}\right) e(251900)e\left(\frac{251}{900}\right)
χ216000(29,)\chi_{216000}(29,\cdot) 216000.yn 3600 yes 1-1 11 e(167360)e\left(\frac{167}{360}\right) e(10073600)e\left(\frac{1007}{3600}\right) e(33733600)e\left(\frac{3373}{3600}\right) e(103300)e\left(\frac{103}{300}\right) e(7671200)e\left(\frac{767}{1200}\right) e(8211800)e\left(\frac{821}{1800}\right) e(2093600)e\left(\frac{209}{3600}\right) e(167450)e\left(\frac{167}{450}\right) e(6011200)e\left(\frac{601}{1200}\right) e(15291800)e\left(\frac{1529}{1800}\right)
χ216000(31,)\chi_{216000}(31,\cdot) 216000.uj 450 no 1-1 11 e(790)e\left(\frac{7}{90}\right) e(208225)e\left(\frac{208}{225}\right) e(49450)e\left(\frac{49}{450}\right) e(5375)e\left(\frac{53}{75}\right) e(7375)e\left(\frac{73}{75}\right) e(271450)e\left(\frac{271}{450}\right) e(167450)e\left(\frac{167}{450}\right) e(343450)e\left(\frac{343}{450}\right) e(13150)e\left(\frac{13}{150}\right) e(2225)e\left(\frac{2}{225}\right)
χ216000(37,)\chi_{216000}(37,\cdot) 216000.xf 1200 no 1-1 11 e(73120)e\left(\frac{73}{120}\right) e(2231200)e\left(\frac{223}{1200}\right) e(4971200)e\left(\frac{497}{1200}\right) e(2325)e\left(\frac{23}{25}\right) e(63400)e\left(\frac{63}{400}\right) e(319600)e\left(\frac{319}{600}\right) e(6011200)e\left(\frac{601}{1200}\right) e(13150)e\left(\frac{13}{150}\right) e(189400)e\left(\frac{189}{400}\right) e(181600)e\left(\frac{181}{600}\right)
χ216000(41,)\chi_{216000}(41,\cdot) 216000.ye 1800 no 1-1 11 e(47180)e\left(\frac{47}{180}\right) e(1671800)e\left(\frac{167}{1800}\right) e(15131800)e\left(\frac{1513}{1800}\right) e(5975)e\left(\frac{59}{75}\right) e(227600)e\left(\frac{227}{600}\right) e(251900)e\left(\frac{251}{900}\right) e(15291800)e\left(\frac{1529}{1800}\right) e(2225)e\left(\frac{2}{225}\right) e(181600)e\left(\frac{181}{600}\right) e(599900)e\left(\frac{599}{900}\right)
χ216000(43,)\chi_{216000}(43,\cdot) 216000.vp 720 no 11 11 e(6772)e\left(\frac{67}{72}\right) e(469720)e\left(\frac{469}{720}\right) e(11720)e\left(\frac{11}{720}\right) e(1330)e\left(\frac{13}{30}\right) e(229240)e\left(\frac{229}{240}\right) e(277360)e\left(\frac{277}{360}\right) e(43720)e\left(\frac{43}{720}\right) e(245)e\left(\frac{2}{45}\right) e(47240)e\left(\frac{47}{240}\right) e(343360)e\left(\frac{343}{360}\right)
χ216000(47,)\chi_{216000}(47,\cdot) 216000.we 900 no 1-1 11 e(121180)e\left(\frac{121}{180}\right) e(23900)e\left(\frac{23}{900}\right) e(43225)e\left(\frac{43}{225}\right) e(193300)e\left(\frac{193}{300}\right) e(263300)e\left(\frac{263}{300}\right) e(313900)e\left(\frac{313}{900}\right) e(701900)e\left(\frac{701}{900}\right) e(377450)e\left(\frac{377}{450}\right) e(1675)e\left(\frac{16}{75}\right) e(178225)e\left(\frac{178}{225}\right)
χ216000(49,)\chi_{216000}(49,\cdot) 216000.qb 180 no 11 11 e(49)e\left(\frac{4}{9}\right) e(101180)e\left(\frac{101}{180}\right) e(49180)e\left(\frac{49}{180}\right) e(2330)e\left(\frac{23}{30}\right) e(4160)e\left(\frac{41}{60}\right) e(3445)e\left(\frac{34}{45}\right) e(167180)e\left(\frac{167}{180}\right) e(745)e\left(\frac{7}{45}\right) e(1360)e\left(\frac{13}{60}\right) e(4790)e\left(\frac{47}{90}\right)
χ216000(53,)\chi_{216000}(53,\cdot) 216000.tu 400 no 11 11 e(340)e\left(\frac{3}{40}\right) e(393400)e\left(\frac{393}{400}\right) e(327400)e\left(\frac{327}{400}\right) e(425)e\left(\frac{4}{25}\right) e(99400)e\left(\frac{99}{400}\right) e(129200)e\left(\frac{129}{200}\right) e(191400)e\left(\frac{191}{400}\right) e(3350)e\left(\frac{33}{50}\right) e(97400)e\left(\frac{97}{400}\right) e(71200)e\left(\frac{71}{200}\right)
χ216000(59,)\chi_{216000}(59,\cdot) 216000.yo 3600 yes 11 11 e(169360)e\left(\frac{169}{360}\right) e(9493600)e\left(\frac{949}{3600}\right) e(15113600)e\left(\frac{1511}{3600}\right) e(221300)e\left(\frac{221}{300}\right) e(4691200)e\left(\frac{469}{1200}\right) e(17471800)e\left(\frac{1747}{1800}\right) e(1633600)e\left(\frac{163}{3600}\right) e(197225)e\left(\frac{197}{225}\right) e(1071200)e\left(\frac{107}{1200}\right) e(10031800)e\left(\frac{1003}{1800}\right)
χ216000(61,)\chi_{216000}(61,\cdot) 216000.ys 3600 yes 11 11 e(251360)e\left(\frac{251}{360}\right) e(1913600)e\left(\frac{191}{3600}\right) e(27493600)e\left(\frac{2749}{3600}\right) e(139300)e\left(\frac{139}{300}\right) e(711200)e\left(\frac{71}{1200}\right) e(13731800)e\left(\frac{1373}{1800}\right) e(24173600)e\left(\frac{2417}{3600}\right) e(71450)e\left(\frac{71}{450}\right) e(3131200)e\left(\frac{313}{1200}\right) e(6771800)e\left(\frac{677}{1800}\right)
χ216000(67,)\chi_{216000}(67,\cdot) 216000.yu 3600 yes 11 11 e(193360)e\left(\frac{193}{360}\right) e(3433600)e\left(\frac{343}{3600}\right) e(15773600)e\left(\frac{1577}{3600}\right) e(61150)e\left(\frac{61}{150}\right) e(5831200)e\left(\frac{583}{1200}\right) e(791800)e\left(\frac{79}{1800}\right) e(20413600)e\left(\frac{2041}{3600}\right) e(29225)e\left(\frac{29}{225}\right) e(1491200)e\left(\frac{149}{1200}\right) e(16211800)e\left(\frac{1621}{1800}\right)
χ216000(71,)\chi_{216000}(71,\cdot) 216000.vg 600 no 11 11 e(1760)e\left(\frac{17}{60}\right) e(107600)e\left(\frac{107}{600}\right) e(73600)e\left(\frac{73}{600}\right) e(1425)e\left(\frac{14}{25}\right) e(167200)e\left(\frac{167}{200}\right) e(221300)e\left(\frac{221}{300}\right) e(209600)e\left(\frac{209}{600}\right) e(109150)e\left(\frac{109}{150}\right) e(101200)e\left(\frac{101}{200}\right) e(179300)e\left(\frac{179}{300}\right)
χ216000(73,)\chi_{216000}(73,\cdot) 216000.uz 600 no 1-1 11 e(2330)e\left(\frac{23}{30}\right) e(421600)e\left(\frac{421}{600}\right) e(269600)e\left(\frac{269}{600}\right) e(93100)e\left(\frac{93}{100}\right) e(1200)e\left(\frac{1}{200}\right) e(119150)e\left(\frac{119}{150}\right) e(127600)e\left(\frac{127}{600}\right) e(175)e\left(\frac{1}{75}\right) e(153200)e\left(\frac{153}{200}\right) e(187300)e\left(\frac{187}{300}\right)
χ216000(77,)\chi_{216000}(77,\cdot) 216000.yx 3600 yes 11 11 e(1360)e\left(\frac{1}{360}\right) e(35713600)e\left(\frac{3571}{3600}\right) e(26693600)e\left(\frac{2669}{3600}\right) e(7175)e\left(\frac{71}{75}\right) e(10511200)e\left(\frac{1051}{1200}\right) e(13631800)e\left(\frac{1363}{1800}\right) e(26773600)e\left(\frac{2677}{3600}\right) e(1450)e\left(\frac{1}{450}\right) e(9531200)e\left(\frac{953}{1200}\right) e(6371800)e\left(\frac{637}{1800}\right)
χ216000(79,)\chi_{216000}(79,\cdot) 216000.ww 900 no 1-1 11 e(5390)e\left(\frac{53}{90}\right) e(263900)e\left(\frac{263}{900}\right) e(157900)e\left(\frac{157}{900}\right) e(29150)e\left(\frac{29}{150}\right) e(203300)e\left(\frac{203}{300}\right) e(239450)e\left(\frac{239}{450}\right) e(131900)e\left(\frac{131}{900}\right) e(437450)e\left(\frac{437}{450}\right) e(109300)e\left(\frac{109}{300}\right) e(11450)e\left(\frac{11}{450}\right)
χ216000(83,)\chi_{216000}(83,\cdot) 216000.yw 3600 yes 1-1 11 e(113360)e\left(\frac{113}{360}\right) e(3233600)e\left(\frac{323}{3600}\right) e(27973600)e\left(\frac{2797}{3600}\right) e(71150)e\left(\frac{71}{150}\right) e(11631200)e\left(\frac{1163}{1200}\right) e(10191800)e\left(\frac{1019}{1800}\right) e(19013600)e\left(\frac{1901}{3600}\right) e(169225)e\left(\frac{169}{225}\right) e(8891200)e\left(\frac{889}{1200}\right) e(17811800)e\left(\frac{1781}{1800}\right)
χ216000(89,)\chi_{216000}(89,\cdot) 216000.vj 600 no 1-1 11 e(160)e\left(\frac{1}{60}\right) e(571600)e\left(\frac{571}{600}\right) e(569600)e\left(\frac{569}{600}\right) e(950)e\left(\frac{9}{50}\right) e(151200)e\left(\frac{151}{200}\right) e(13300)e\left(\frac{13}{300}\right) e(277600)e\left(\frac{277}{600}\right) e(175)e\left(\frac{1}{75}\right) e(53200)e\left(\frac{53}{200}\right) e(187300)e\left(\frac{187}{300}\right)
χ216000(91,)\chi_{216000}(91,\cdot) 216000.xj 1200 no 1-1 11 e(103120)e\left(\frac{103}{120}\right) e(10631200)e\left(\frac{1063}{1200}\right) e(5571200)e\left(\frac{557}{1200}\right) e(27100)e\left(\frac{27}{100}\right) e(303400)e\left(\frac{303}{400}\right) e(289600)e\left(\frac{289}{600}\right) e(4811200)e\left(\frac{481}{1200}\right) e(1475)e\left(\frac{14}{75}\right) e(9400)e\left(\frac{9}{400}\right) e(61600)e\left(\frac{61}{600}\right)
χ216000(97,)\chi_{216000}(97,\cdot) 216000.wo 900 no 1-1 11 e(1180)e\left(\frac{1}{180}\right) e(229450)e\left(\frac{229}{450}\right) e(637900)e\left(\frac{637}{900}\right) e(103300)e\left(\frac{103}{300}\right) e(6275)e\left(\frac{62}{75}\right) e(823900)e\left(\frac{823}{900}\right) e(149225)e\left(\frac{149}{225}\right) e(46225)e\left(\frac{46}{225}\right) e(169300)e\left(\frac{169}{300}\right) e(13225)e\left(\frac{13}{225}\right)
χ216000(101,)\chi_{216000}(101,\cdot) 216000.vx 720 no 1-1 11 e(6172)e\left(\frac{61}{72}\right) e(337720)e\left(\frac{337}{720}\right) e(683720)e\left(\frac{683}{720}\right) e(2360)e\left(\frac{23}{60}\right) e(97240)e\left(\frac{97}{240}\right) e(271360)e\left(\frac{271}{360}\right) e(559720)e\left(\frac{559}{720}\right) e(790)e\left(\frac{7}{90}\right) e(191240)e\left(\frac{191}{240}\right) e(319360)e\left(\frac{319}{360}\right)
χ216000(103,)\chi_{216000}(103,\cdot) 216000.xw 1800 no 11 11 e(1390)e\left(\frac{13}{90}\right) e(13611800)e\left(\frac{1361}{1800}\right) e(11291800)e\left(\frac{1129}{1800}\right) e(263300)e\left(\frac{263}{300}\right) e(341600)e\left(\frac{341}{600}\right) e(79450)e\left(\frac{79}{450}\right) e(16071800)e\left(\frac{1607}{1800}\right) e(7450)e\left(\frac{7}{450}\right) e(373600)e\left(\frac{373}{600}\right) e(767900)e\left(\frac{767}{900}\right)
χ216000(107,)\chi_{216000}(107,\cdot) 216000.mo 80 no 1-1 11 e(78)e\left(\frac{7}{8}\right) e(3780)e\left(\frac{37}{80}\right) e(4380)e\left(\frac{43}{80}\right) e(710)e\left(\frac{7}{10}\right) e(7180)e\left(\frac{71}{80}\right) e(2140)e\left(\frac{21}{40}\right) e(5980)e\left(\frac{59}{80}\right) e(15)e\left(\frac{1}{5}\right) e(1380)e\left(\frac{13}{80}\right) e(1940)e\left(\frac{19}{40}\right)
χ216000(109,)\chi_{216000}(109,\cdot) 216000.tz 400 no 11 11 e(1140)e\left(\frac{11}{40}\right) e(91400)e\left(\frac{91}{400}\right) e(249400)e\left(\frac{249}{400}\right) e(67100)e\left(\frac{67}{100}\right) e(313400)e\left(\frac{313}{400}\right) e(173200)e\left(\frac{173}{200}\right) e(117400)e\left(\frac{117}{400}\right) e(2150)e\left(\frac{21}{50}\right) e(239400)e\left(\frac{239}{400}\right) e(177200)e\left(\frac{177}{200}\right)
χ216000(113,)\chi_{216000}(113,\cdot) 216000.xb 900 no 11 11 e(17180)e\left(\frac{17}{180}\right) e(631900)e\left(\frac{631}{900}\right) e(221225)e\left(\frac{221}{225}\right) e(71300)e\left(\frac{71}{300}\right) e(211300)e\left(\frac{211}{300}\right) e(761900)e\left(\frac{761}{900}\right) e(547900)e\left(\frac{547}{900}\right) e(197225)e\left(\frac{197}{225}\right) e(275)e\left(\frac{2}{75}\right) e(41225)e\left(\frac{41}{225}\right)
χ216000(119,)\chi_{216000}(119,\cdot) 216000.yf 1800 no 11 11 e(19180)e\left(\frac{19}{180}\right) e(15191800)e\left(\frac{1519}{1800}\right) e(411800)e\left(\frac{41}{1800}\right) e(101150)e\left(\frac{101}{150}\right) e(139600)e\left(\frac{139}{600}\right) e(607900)e\left(\frac{607}{900}\right) e(14531800)e\left(\frac{1453}{1800}\right) e(353450)e\left(\frac{353}{450}\right) e(317600)e\left(\frac{317}{600}\right) e(43900)e\left(\frac{43}{900}\right)
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