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Properties

Modulus 3686436864
Structure C2×C2×C3072C_{2}\times C_{2}\times C_{3072}
Order 1228812288

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(36864)
 
pari: g = idealstar(,36864,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 12288
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C3072C_{2}\times C_{2}\times C_{3072}
sage: H.gens()
 
pari: g.gen
 
Generators = χ36864(8191,⋅)\chi_{36864}(8191,\cdot), χ36864(20485,⋅)\chi_{36864}(20485,\cdot), χ36864(4097,⋅)\chi_{36864}(4097,\cdot)

First 32 of 12288 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
χ36864(1,⋅)\chi_{36864}(1,\cdot) 36864.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ36864(5,⋅)\chi_{36864}(5,\cdot) 36864.dj 3072 yes −1-1 11 e(5153072)e\left(\frac{515}{3072}\right) e(471536)e\left(\frac{47}{1536}\right) e(1273072)e\left(\frac{127}{3072}\right) e(19973072)e\left(\frac{1997}{3072}\right) e(231256)e\left(\frac{231}{256}\right) e(9191024)e\left(\frac{919}{1024}\right) e(4691536)e\left(\frac{469}{1536}\right) e(5151536)e\left(\frac{515}{1536}\right) e(21613072)e\left(\frac{2161}{3072}\right) e(19384)e\left(\frac{19}{384}\right)
χ36864(7,⋅)\chi_{36864}(7,\cdot) 36864.dd 1536 no −1-1 11 e(471536)e\left(\frac{47}{1536}\right) e(11768)e\left(\frac{11}{768}\right) e(10511536)e\left(\frac{1051}{1536}\right) e(7371536)e\left(\frac{737}{1536}\right) e(35128)e\left(\frac{35}{128}\right) e(147512)e\left(\frac{147}{512}\right) e(649768)e\left(\frac{649}{768}\right) e(47768)e\left(\frac{47}{768}\right) e(14291536)e\left(\frac{1429}{1536}\right) e(31192)e\left(\frac{31}{192}\right)
χ36864(11,⋅)\chi_{36864}(11,\cdot) 36864.dh 3072 yes 11 11 e(1273072)e\left(\frac{127}{3072}\right) e(10511536)e\left(\frac{1051}{1536}\right) e(29873072)e\left(\frac{2987}{3072}\right) e(24493072)e\left(\frac{2449}{3072}\right) e(51256)e\left(\frac{51}{256}\right) e(6751024)e\left(\frac{675}{1024}\right) e(13371536)e\left(\frac{1337}{1536}\right) e(1271536)e\left(\frac{127}{1536}\right) e(15413072)e\left(\frac{1541}{3072}\right) e(143384)e\left(\frac{143}{384}\right)
χ36864(13,⋅)\chi_{36864}(13,\cdot) 36864.di 3072 yes 11 11 e(19973072)e\left(\frac{1997}{3072}\right) e(7371536)e\left(\frac{737}{1536}\right) e(24493072)e\left(\frac{2449}{3072}\right) e(29153072)e\left(\frac{2915}{3072}\right) e(41256)e\left(\frac{41}{256}\right) e(7611024)e\left(\frac{761}{1024}\right) e(4751536)e\left(\frac{475}{1536}\right) e(4611536)e\left(\frac{461}{1536}\right) e(16633072)e\left(\frac{1663}{3072}\right) e(61384)e\left(\frac{61}{384}\right)
χ36864(17,⋅)\chi_{36864}(17,\cdot) 36864.ci 256 no −1-1 11 e(231256)e\left(\frac{231}{256}\right) e(35128)e\left(\frac{35}{128}\right) e(51256)e\left(\frac{51}{256}\right) e(41256)e\left(\frac{41}{256}\right) e(1764)e\left(\frac{17}{64}\right) e(193256)e\left(\frac{193}{256}\right) e(81128)e\left(\frac{81}{128}\right) e(103128)e\left(\frac{103}{128}\right) e(253256)e\left(\frac{253}{256}\right) e(2332)e\left(\frac{23}{32}\right)
χ36864(19,⋅)\chi_{36864}(19,\cdot) 36864.db 1024 no −1-1 11 e(9191024)e\left(\frac{919}{1024}\right) e(147512)e\left(\frac{147}{512}\right) e(6751024)e\left(\frac{675}{1024}\right) e(7611024)e\left(\frac{761}{1024}\right) e(193256)e\left(\frac{193}{256}\right) e(2731024)e\left(\frac{273}{1024}\right) e(481512)e\left(\frac{481}{512}\right) e(407512)e\left(\frac{407}{512}\right) e(6531024)e\left(\frac{653}{1024}\right) e(39128)e\left(\frac{39}{128}\right)
χ36864(23,⋅)\chi_{36864}(23,\cdot) 36864.df 1536 no 11 11 e(4691536)e\left(\frac{469}{1536}\right) e(649768)e\left(\frac{649}{768}\right) e(13371536)e\left(\frac{1337}{1536}\right) e(4751536)e\left(\frac{475}{1536}\right) e(81128)e\left(\frac{81}{128}\right) e(481512)e\left(\frac{481}{512}\right) e(275768)e\left(\frac{275}{768}\right) e(469768)e\left(\frac{469}{768}\right) e(5991536)e\left(\frac{599}{1536}\right) e(101192)e\left(\frac{101}{192}\right)
χ36864(25,⋅)\chi_{36864}(25,\cdot) 36864.dc 1536 no 11 11 e(5151536)e\left(\frac{515}{1536}\right) e(47768)e\left(\frac{47}{768}\right) e(1271536)e\left(\frac{127}{1536}\right) e(4611536)e\left(\frac{461}{1536}\right) e(103128)e\left(\frac{103}{128}\right) e(407512)e\left(\frac{407}{512}\right) e(469768)e\left(\frac{469}{768}\right) e(515768)e\left(\frac{515}{768}\right) e(6251536)e\left(\frac{625}{1536}\right) e(19192)e\left(\frac{19}{192}\right)
χ36864(29,⋅)\chi_{36864}(29,\cdot) 36864.dj 3072 yes −1-1 11 e(21613072)e\left(\frac{2161}{3072}\right) e(14291536)e\left(\frac{1429}{1536}\right) e(15413072)e\left(\frac{1541}{3072}\right) e(16633072)e\left(\frac{1663}{3072}\right) e(253256)e\left(\frac{253}{256}\right) e(6531024)e\left(\frac{653}{1024}\right) e(5991536)e\left(\frac{599}{1536}\right) e(6251536)e\left(\frac{625}{1536}\right) e(13553072)e\left(\frac{1355}{3072}\right) e(161384)e\left(\frac{161}{384}\right)
χ36864(31,⋅)\chi_{36864}(31,\cdot) 36864.cp 384 no −1-1 11 e(19384)e\left(\frac{19}{384}\right) e(31192)e\left(\frac{31}{192}\right) e(143384)e\left(\frac{143}{384}\right) e(61384)e\left(\frac{61}{384}\right) e(2332)e\left(\frac{23}{32}\right) e(39128)e\left(\frac{39}{128}\right) e(101192)e\left(\frac{101}{192}\right) e(19192)e\left(\frac{19}{192}\right) e(161384)e\left(\frac{161}{384}\right) e(1148)e\left(\frac{11}{48}\right)
χ36864(35,⋅)\chi_{36864}(35,\cdot) 36864.da 1024 no 11 11 e(2031024)e\left(\frac{203}{1024}\right) e(23512)e\left(\frac{23}{512}\right) e(7431024)e\left(\frac{743}{1024}\right) e(1331024)e\left(\frac{133}{1024}\right) e(45256)e\left(\frac{45}{256}\right) e(1891024)e\left(\frac{189}{1024}\right) e(77512)e\left(\frac{77}{512}\right) e(203512)e\left(\frac{203}{512}\right) e(6491024)e\left(\frac{649}{1024}\right) e(27128)e\left(\frac{27}{128}\right)
χ36864(37,⋅)\chi_{36864}(37,\cdot) 36864.cz 1024 no 11 11 e(2811024)e\left(\frac{281}{1024}\right) e(477512)e\left(\frac{477}{512}\right) e(4611024)e\left(\frac{461}{1024}\right) e(3431024)e\left(\frac{343}{1024}\right) e(15256)e\left(\frac{15}{256}\right) e(1911024)e\left(\frac{191}{1024}\right) e(495512)e\left(\frac{495}{512}\right) e(281512)e\left(\frac{281}{512}\right) e(5151024)e\left(\frac{515}{1024}\right) e(73128)e\left(\frac{73}{128}\right)
χ36864(41,⋅)\chi_{36864}(41,\cdot) 36864.de 1536 no −1-1 11 e(14051536)e\left(\frac{1405}{1536}\right) e(337768)e\left(\frac{337}{768}\right) e(2571536)e\left(\frac{257}{1536}\right) e(14591536)e\left(\frac{1459}{1536}\right) e(89128)e\left(\frac{89}{128}\right) e(233512)e\left(\frac{233}{512}\right) e(299768)e\left(\frac{299}{768}\right) e(637768)e\left(\frac{637}{768}\right) e(5271536)e\left(\frac{527}{1536}\right) e(173192)e\left(\frac{173}{192}\right)
χ36864(43,⋅)\chi_{36864}(43,\cdot) 36864.dg 3072 yes −1-1 11 e(19753072)e\left(\frac{1975}{3072}\right) e(3071536)e\left(\frac{307}{1536}\right) e(3233072)e\left(\frac{323}{3072}\right) e(2173072)e\left(\frac{217}{3072}\right) e(139256)e\left(\frac{139}{256}\right) e(10191024)e\left(\frac{1019}{1024}\right) e(12171536)e\left(\frac{1217}{1536}\right) e(4391536)e\left(\frac{439}{1536}\right) e(15173072)e\left(\frac{1517}{3072}\right) e(71384)e\left(\frac{71}{384}\right)
χ36864(47,⋅)\chi_{36864}(47,\cdot) 36864.cu 768 no 11 11 e(1768)e\left(\frac{1}{768}\right) e(37384)e\left(\frac{37}{384}\right) e(341768)e\left(\frac{341}{768}\right) e(367768)e\left(\frac{367}{768}\right) e(4564)e\left(\frac{45}{64}\right) e(221256)e\left(\frac{221}{256}\right) e(71384)e\left(\frac{71}{384}\right) e(1384)e\left(\frac{1}{384}\right) e(635768)e\left(\frac{635}{768}\right) e(6596)e\left(\frac{65}{96}\right)
χ36864(49,⋅)\chi_{36864}(49,\cdot) 36864.cx 768 no 11 11 e(47768)e\left(\frac{47}{768}\right) e(11384)e\left(\frac{11}{384}\right) e(283768)e\left(\frac{283}{768}\right) e(737768)e\left(\frac{737}{768}\right) e(3564)e\left(\frac{35}{64}\right) e(147256)e\left(\frac{147}{256}\right) e(265384)e\left(\frac{265}{384}\right) e(47384)e\left(\frac{47}{384}\right) e(661768)e\left(\frac{661}{768}\right) e(3196)e\left(\frac{31}{96}\right)
χ36864(53,⋅)\chi_{36864}(53,\cdot) 36864.cy 1024 no −1-1 11 e(2611024)e\left(\frac{261}{1024}\right) e(505512)e\left(\frac{505}{512}\right) e(2971024)e\left(\frac{297}{1024}\right) e(1711024)e\left(\frac{171}{1024}\right) e(131256)e\left(\frac{131}{256}\right) e(7551024)e\left(\frac{755}{1024}\right) e(355512)e\left(\frac{355}{512}\right) e(261512)e\left(\frac{261}{512}\right) e(1031024)e\left(\frac{103}{1024}\right) e(117128)e\left(\frac{117}{128}\right)
χ36864(55,⋅)\chi_{36864}(55,\cdot) 36864.cq 512 no −1-1 11 e(107512)e\left(\frac{107}{512}\right) e(183256)e\left(\frac{183}{256}\right) e(7512)e\left(\frac{7}{512}\right) e(229512)e\left(\frac{229}{512}\right) e(13128)e\left(\frac{13}{128}\right) e(285512)e\left(\frac{285}{512}\right) e(45256)e\left(\frac{45}{256}\right) e(107256)e\left(\frac{107}{256}\right) e(105512)e\left(\frac{105}{512}\right) e(2764)e\left(\frac{27}{64}\right)
χ36864(59,⋅)\chi_{36864}(59,\cdot) 36864.dh 3072 yes 11 11 e(11393072)e\left(\frac{1139}{3072}\right) e(8631536)e\left(\frac{863}{1536}\right) e(24793072)e\left(\frac{2479}{3072}\right) e(6053072)e\left(\frac{605}{3072}\right) e(151256)e\left(\frac{151}{256}\right) e(711024)e\left(\frac{71}{1024}\right) e(9971536)e\left(\frac{997}{1536}\right) e(11391536)e\left(\frac{1139}{1536}\right) e(21133072)e\left(\frac{2113}{3072}\right) e(67384)e\left(\frac{67}{384}\right)
χ36864(61,⋅)\chi_{36864}(61,\cdot) 36864.di 3072 yes 11 11 e(20413072)e\left(\frac{2041}{3072}\right) e(611536)e\left(\frac{61}{1536}\right) e(5573072)e\left(\frac{557}{3072}\right) e(21673072)e\left(\frac{2167}{3072}\right) e(101256)e\left(\frac{101}{256}\right) e(2451024)e\left(\frac{245}{1024}\right) e(5271536)e\left(\frac{527}{1536}\right) e(5051536)e\left(\frac{505}{1536}\right) e(19553072)e\left(\frac{1955}{3072}\right) e(41384)e\left(\frac{41}{384}\right)
χ36864(65,⋅)\chi_{36864}(65,\cdot) 36864.cf 192 no −1-1 11 e(157192)e\left(\frac{157}{192}\right) e(4996)e\left(\frac{49}{96}\right) e(161192)e\left(\frac{161}{192}\right) e(115192)e\left(\frac{115}{192}\right) e(116)e\left(\frac{1}{16}\right) e(4164)e\left(\frac{41}{64}\right) e(5996)e\left(\frac{59}{96}\right) e(6196)e\left(\frac{61}{96}\right) e(47192)e\left(\frac{47}{192}\right) e(524)e\left(\frac{5}{24}\right)
χ36864(67,⋅)\chi_{36864}(67,\cdot) 36864.dg 3072 yes −1-1 11 e(20093072)e\left(\frac{2009}{3072}\right) e(11811536)e\left(\frac{1181}{1536}\right) e(3973072)e\left(\frac{397}{3072}\right) e(27113072)e\left(\frac{2711}{3072}\right) e(197256)e\left(\frac{197}{256}\right) e(8531024)e\left(\frac{853}{1024}\right) e(5591536)e\left(\frac{559}{1536}\right) e(4731536)e\left(\frac{473}{1536}\right) e(673072)e\left(\frac{67}{3072}\right) e(73384)e\left(\frac{73}{384}\right)
χ36864(71,⋅)\chi_{36864}(71,\cdot) 36864.cs 512 no 11 11 e(173512)e\left(\frac{173}{512}\right) e(193256)e\left(\frac{193}{256}\right) e(241512)e\left(\frac{241}{512}\right) e(387512)e\left(\frac{387}{512}\right) e(91128)e\left(\frac{91}{128}\right) e(267512)e\left(\frac{267}{512}\right) e(251256)e\left(\frac{251}{256}\right) e(173256)e\left(\frac{173}{256}\right) e(31512)e\left(\frac{31}{512}\right) e(6164)e\left(\frac{61}{64}\right)
χ36864(73,⋅)\chi_{36864}(73,\cdot) 36864.cr 512 no 11 11 e(219512)e\left(\frac{219}{512}\right) e(103256)e\left(\frac{103}{256}\right) e(55512)e\left(\frac{55}{512}\right) e(373512)e\left(\frac{373}{512}\right) e(29128)e\left(\frac{29}{128}\right) e(45512)e\left(\frac{45}{512}\right) e(189256)e\left(\frac{189}{256}\right) e(219256)e\left(\frac{219}{256}\right) e(57512)e\left(\frac{57}{512}\right) e(4364)e\left(\frac{43}{64}\right)
χ36864(77,⋅)\chi_{36864}(77,\cdot) 36864.dj 3072 yes −1-1 11 e(2213072)e\left(\frac{221}{3072}\right) e(10731536)e\left(\frac{1073}{1536}\right) e(20173072)e\left(\frac{2017}{3072}\right) e(8513072)e\left(\frac{851}{3072}\right) e(121256)e\left(\frac{121}{256}\right) e(9691024)e\left(\frac{969}{1024}\right) e(10991536)e\left(\frac{1099}{1536}\right) e(2211536)e\left(\frac{221}{1536}\right) e(13273072)e\left(\frac{1327}{3072}\right) e(205384)e\left(\frac{205}{384}\right)
χ36864(79,⋅)\chi_{36864}(79,\cdot) 36864.cv 768 no −1-1 11 e(199768)e\left(\frac{199}{768}\right) e(67384)e\left(\frac{67}{384}\right) e(275768)e\left(\frac{275}{768}\right) e(457768)e\left(\frac{457}{768}\right) e(2764)e\left(\frac{27}{64}\right) e(75256)e\left(\frac{75}{256}\right) e(113384)e\left(\frac{113}{384}\right) e(199384)e\left(\frac{199}{384}\right) e(413768)e\left(\frac{413}{768}\right) e(7196)e\left(\frac{71}{96}\right)
χ36864(83,⋅)\chi_{36864}(83,\cdot) 36864.dh 3072 yes 11 11 e(9493072)e\left(\frac{949}{3072}\right) e(11291536)e\left(\frac{1129}{1536}\right) e(29693072)e\left(\frac{2969}{3072}\right) e(7633072)e\left(\frac{763}{3072}\right) e(113256)e\left(\frac{113}{256}\right) e(5771024)e\left(\frac{577}{1024}\right) e(13311536)e\left(\frac{1331}{1536}\right) e(9491536)e\left(\frac{949}{1536}\right) e(28073072)e\left(\frac{2807}{3072}\right) e(101384)e\left(\frac{101}{384}\right)
χ36864(85,⋅)\chi_{36864}(85,\cdot) 36864.di 3072 yes 11 11 e(2153072)e\left(\frac{215}{3072}\right) e(4671536)e\left(\frac{467}{1536}\right) e(7393072)e\left(\frac{739}{3072}\right) e(24893072)e\left(\frac{2489}{3072}\right) e(43256)e\left(\frac{43}{256}\right) e(6671024)e\left(\frac{667}{1024}\right) e(14411536)e\left(\frac{1441}{1536}\right) e(2151536)e\left(\frac{215}{1536}\right) e(21253072)e\left(\frac{2125}{3072}\right) e(295384)e\left(\frac{295}{384}\right)
χ36864(89,⋅)\chi_{36864}(89,\cdot) 36864.ct 512 no −1-1 11 e(441512)e\left(\frac{441}{512}\right) e(253256)e\left(\frac{253}{256}\right) e(237512)e\left(\frac{237}{512}\right) e(439512)e\left(\frac{439}{512}\right) e(47128)e\left(\frac{47}{128}\right) e(31512)e\left(\frac{31}{512}\right) e(207256)e\left(\frac{207}{256}\right) e(185256)e\left(\frac{185}{256}\right) e(227512)e\left(\frac{227}{512}\right) e(4164)e\left(\frac{41}{64}\right)
χ36864(91,⋅)\chi_{36864}(91,\cdot) 36864.db 1024 no −1-1 11 e(6971024)e\left(\frac{697}{1024}\right) e(253512)e\left(\frac{253}{512}\right) e(4931024)e\left(\frac{493}{1024}\right) e(4391024)e\left(\frac{439}{1024}\right) e(111256)e\left(\frac{111}{256}\right) e(311024)e\left(\frac{31}{1024}\right) e(79512)e\left(\frac{79}{512}\right) e(185512)e\left(\frac{185}{512}\right) e(4831024)e\left(\frac{483}{1024}\right) e(41128)e\left(\frac{41}{128}\right)
χ36864(95,⋅)\chi_{36864}(95,\cdot) 36864.cn 384 no 11 11 e(25384)e\left(\frac{25}{384}\right) e(61192)e\left(\frac{61}{192}\right) e(269384)e\left(\frac{269}{384}\right) e(151384)e\left(\frac{151}{384}\right) e(2132)e\left(\frac{21}{32}\right) e(21128)e\left(\frac{21}{128}\right) e(47192)e\left(\frac{47}{192}\right) e(25192)e\left(\frac{25}{192}\right) e(131384)e\left(\frac{131}{384}\right) e(1748)e\left(\frac{17}{48}\right)
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