Properties

Modulus 259200259200
Structure C2×C2×C4×C4320C_{2}\times C_{2}\times C_{4}\times C_{4320}
Order 6912069120

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(259200)
 
pari: g = idealstar(,259200,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 69120
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C4×C4320C_{2}\times C_{2}\times C_{4}\times C_{4320}
sage: H.gens()
 
pari: g.gen
 
Generators = χ259200(157951,)\chi_{259200}(157951,\cdot), χ259200(202501,)\chi_{259200}(202501,\cdot), χ259200(6401,)\chi_{259200}(6401,\cdot), χ259200(72577,)\chi_{259200}(72577,\cdot)

First 32 of 69120 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
χ259200(1,)\chi_{259200}(1,\cdot) 259200.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ259200(7,)\chi_{259200}(7,\cdot) 259200.vg 432 no 11 11 e(133216)e\left(\frac{133}{216}\right) e(395432)e\left(\frac{395}{432}\right) e(349432)e\left(\frac{349}{432}\right) e(79)e\left(\frac{7}{9}\right) e(59144)e\left(\frac{59}{144}\right) e(191216)e\left(\frac{191}{216}\right) e(389432)e\left(\frac{389}{432}\right) e(2527)e\left(\frac{25}{27}\right) e(73144)e\left(\frac{73}{144}\right) e(17216)e\left(\frac{17}{216}\right)
χ259200(11,)\chi_{259200}(11,\cdot) 259200.baz 4320 yes 11 11 e(395432)e\left(\frac{395}{432}\right) e(9114320)e\left(\frac{911}{4320}\right) e(41894320)e\left(\frac{4189}{4320}\right) e(259360)e\left(\frac{259}{360}\right) e(7911440)e\left(\frac{791}{1440}\right) e(2932160)e\left(\frac{293}{2160}\right) e(9774320)e\left(\frac{977}{4320}\right) e(521540)e\left(\frac{521}{540}\right) e(10331440)e\left(\frac{1033}{1440}\right) e(13972160)e\left(\frac{1397}{2160}\right)
χ259200(13,)\chi_{259200}(13,\cdot) 259200.baq 4320 yes 1-1 11 e(349432)e\left(\frac{349}{432}\right) e(41894320)e\left(\frac{4189}{4320}\right) e(11514320)e\left(\frac{1151}{4320}\right) e(131360)e\left(\frac{131}{360}\right) e(14291440)e\left(\frac{1429}{1440}\right) e(13872160)e\left(\frac{1387}{2160}\right) e(1634320)e\left(\frac{163}{4320}\right) e(169540)e\left(\frac{169}{540}\right) e(7071440)e\left(\frac{707}{1440}\right) e(15432160)e\left(\frac{1543}{2160}\right)
χ259200(17,)\chi_{259200}(17,\cdot) 259200.vb 360 no 11 11 e(79)e\left(\frac{7}{9}\right) e(259360)e\left(\frac{259}{360}\right) e(131360)e\left(\frac{131}{360}\right) e(760)e\left(\frac{7}{60}\right) e(19120)e\left(\frac{19}{120}\right) e(1190)e\left(\frac{11}{90}\right) e(193360)e\left(\frac{193}{360}\right) e(1945)e\left(\frac{19}{45}\right) e(47120)e\left(\frac{47}{120}\right) e(43180)e\left(\frac{43}{180}\right)
χ259200(19,)\chi_{259200}(19,\cdot) 259200.zv 1440 no 1-1 11 e(59144)e\left(\frac{59}{144}\right) e(7911440)e\left(\frac{791}{1440}\right) e(14291440)e\left(\frac{1429}{1440}\right) e(19120)e\left(\frac{19}{120}\right) e(431480)e\left(\frac{431}{480}\right) e(173720)e\left(\frac{173}{720}\right) e(1371440)e\left(\frac{137}{1440}\right) e(41180)e\left(\frac{41}{180}\right) e(193480)e\left(\frac{193}{480}\right) e(197720)e\left(\frac{197}{720}\right)
χ259200(23,)\chi_{259200}(23,\cdot) 259200.bad 2160 no 1-1 11 e(191216)e\left(\frac{191}{216}\right) e(2932160)e\left(\frac{293}{2160}\right) e(13872160)e\left(\frac{1387}{2160}\right) e(1190)e\left(\frac{11}{90}\right) e(173720)e\left(\frac{173}{720}\right) e(9891080)e\left(\frac{989}{1080}\right) e(9712160)e\left(\frac{971}{2160}\right) e(64135)e\left(\frac{64}{135}\right) e(319720)e\left(\frac{319}{720}\right) e(1311080)e\left(\frac{131}{1080}\right)
χ259200(29,)\chi_{259200}(29,\cdot) 259200.bay 4320 yes 1-1 11 e(389432)e\left(\frac{389}{432}\right) e(9774320)e\left(\frac{977}{4320}\right) e(1634320)e\left(\frac{163}{4320}\right) e(193360)e\left(\frac{193}{360}\right) e(1371440)e\left(\frac{137}{1440}\right) e(9712160)e\left(\frac{971}{2160}\right) e(14394320)e\left(\frac{1439}{4320}\right) e(137540)e\left(\frac{137}{540}\right) e(11111440)e\left(\frac{1111}{1440}\right) e(592160)e\left(\frac{59}{2160}\right)
χ259200(31,)\chi_{259200}(31,\cdot) 259200.wu 540 no 1-1 11 e(2527)e\left(\frac{25}{27}\right) e(521540)e\left(\frac{521}{540}\right) e(169540)e\left(\frac{169}{540}\right) e(1945)e\left(\frac{19}{45}\right) e(41180)e\left(\frac{41}{180}\right) e(64135)e\left(\frac{64}{135}\right) e(137540)e\left(\frac{137}{540}\right) e(29270)e\left(\frac{29}{270}\right) e(73180)e\left(\frac{73}{180}\right) e(197270)e\left(\frac{197}{270}\right)
χ259200(37,)\chi_{259200}(37,\cdot) 259200.zk 1440 no 1-1 11 e(73144)e\left(\frac{73}{144}\right) e(10331440)e\left(\frac{1033}{1440}\right) e(7071440)e\left(\frac{707}{1440}\right) e(47120)e\left(\frac{47}{120}\right) e(193480)e\left(\frac{193}{480}\right) e(319720)e\left(\frac{319}{720}\right) e(11111440)e\left(\frac{1111}{1440}\right) e(73180)e\left(\frac{73}{180}\right) e(119480)e\left(\frac{119}{480}\right) e(331720)e\left(\frac{331}{720}\right)
χ259200(41,)\chi_{259200}(41,\cdot) 259200.baa 2160 no 1-1 11 e(17216)e\left(\frac{17}{216}\right) e(13972160)e\left(\frac{1397}{2160}\right) e(15432160)e\left(\frac{1543}{2160}\right) e(43180)e\left(\frac{43}{180}\right) e(197720)e\left(\frac{197}{720}\right) e(1311080)e\left(\frac{131}{1080}\right) e(592160)e\left(\frac{59}{2160}\right) e(197270)e\left(\frac{197}{270}\right) e(331720)e\left(\frac{331}{720}\right) e(10191080)e\left(\frac{1019}{1080}\right)
χ259200(43,)\chi_{259200}(43,\cdot) 259200.yk 864 no 11 11 e(359432)e\left(\frac{359}{432}\right) e(715864)e\left(\frac{715}{864}\right) e(89864)e\left(\frac{89}{864}\right) e(4172)e\left(\frac{41}{72}\right) e(115288)e\left(\frac{115}{288}\right) e(397432)e\left(\frac{397}{432}\right) e(37864)e\left(\frac{37}{864}\right) e(97108)e\left(\frac{97}{108}\right) e(149288)e\left(\frac{149}{288}\right) e(337432)e\left(\frac{337}{432}\right)
χ259200(47,)\chi_{259200}(47,\cdot) 259200.zf 1080 no 1-1 11 e(3154)e\left(\frac{31}{54}\right) e(7131080)e\left(\frac{713}{1080}\right) e(8771080)e\left(\frac{877}{1080}\right) e(149180)e\left(\frac{149}{180}\right) e(233360)e\left(\frac{233}{360}\right) e(71135)e\left(\frac{71}{135}\right) e(6711080)e\left(\frac{671}{1080}\right) e(241270)e\left(\frac{241}{270}\right) e(169360)e\left(\frac{169}{360}\right) e(281540)e\left(\frac{281}{540}\right)
χ259200(49,)\chi_{259200}(49,\cdot) 259200.sr 216 no 11 11 e(25108)e\left(\frac{25}{108}\right) e(179216)e\left(\frac{179}{216}\right) e(133216)e\left(\frac{133}{216}\right) e(59)e\left(\frac{5}{9}\right) e(5972)e\left(\frac{59}{72}\right) e(83108)e\left(\frac{83}{108}\right) e(173216)e\left(\frac{173}{216}\right) e(2327)e\left(\frac{23}{27}\right) e(172)e\left(\frac{1}{72}\right) e(17108)e\left(\frac{17}{108}\right)
χ259200(53,)\chi_{259200}(53,\cdot) 259200.wl 480 no 11 11 e(3148)e\left(\frac{31}{48}\right) e(343480)e\left(\frac{343}{480}\right) e(317480)e\left(\frac{317}{480}\right) e(1740)e\left(\frac{17}{40}\right) e(143160)e\left(\frac{143}{160}\right) e(49240)e\left(\frac{49}{240}\right) e(361480)e\left(\frac{361}{480}\right) e(4360)e\left(\frac{43}{60}\right) e(9160)e\left(\frac{9}{160}\right) e(61240)e\left(\frac{61}{240}\right)
χ259200(59,)\chi_{259200}(59,\cdot) 259200.bap 4320 yes 11 11 e(199432)e\left(\frac{199}{432}\right) e(31394320)e\left(\frac{3139}{4320}\right) e(14814320)e\left(\frac{1481}{4320}\right) e(11360)e\left(\frac{11}{360}\right) e(10991440)e\left(\frac{1099}{1440}\right) e(21372160)e\left(\frac{2137}{2160}\right) e(36134320)e\left(\frac{3613}{4320}\right) e(289540)e\left(\frac{289}{540}\right) e(6771440)e\left(\frac{677}{1440}\right) e(21132160)e\left(\frac{2113}{2160}\right)
χ259200(61,)\chi_{259200}(61,\cdot) 259200.bam 4320 yes 11 11 e(149432)e\left(\frac{149}{432}\right) e(34014320)e\left(\frac{3401}{4320}\right) e(34994320)e\left(\frac{3499}{4320}\right) e(289360)e\left(\frac{289}{360}\right) e(4011440)e\left(\frac{401}{1440}\right) e(15232160)e\left(\frac{1523}{2160}\right) e(11274320)e\left(\frac{1127}{4320}\right) e(221540)e\left(\frac{221}{540}\right) e(7031440)e\left(\frac{703}{1440}\right) e(1072160)e\left(\frac{107}{2160}\right)
χ259200(67,)\chi_{259200}(67,\cdot) 259200.bar 4320 yes 11 11 e(313432)e\left(\frac{313}{432}\right) e(41534320)e\left(\frac{4153}{4320}\right) e(33474320)e\left(\frac{3347}{4320}\right) e(347360)e\left(\frac{347}{360}\right) e(13931440)e\left(\frac{1393}{1440}\right) e(19992160)e\left(\frac{1999}{2160}\right) e(20714320)e\left(\frac{2071}{4320}\right) e(403540)e\left(\frac{403}{540}\right) e(13191440)e\left(\frac{1319}{1440}\right) e(12912160)e\left(\frac{1291}{2160}\right)
χ259200(71,)\chi_{259200}(71,\cdot) 259200.xp 720 no 11 11 e(5372)e\left(\frac{53}{72}\right) e(317720)e\left(\frac{317}{720}\right) e(103720)e\left(\frac{103}{720}\right) e(4360)e\left(\frac{43}{60}\right) e(77240)e\left(\frac{77}{240}\right) e(311360)e\left(\frac{311}{360}\right) e(59720)e\left(\frac{59}{720}\right) e(3145)e\left(\frac{31}{45}\right) e(91240)e\left(\frac{91}{240}\right) e(299360)e\left(\frac{299}{360}\right)
χ259200(73,)\chi_{259200}(73,\cdot) 259200.xx 720 no 1-1 11 e(3772)e\left(\frac{37}{72}\right) e(331720)e\left(\frac{331}{720}\right) e(149720)e\left(\frac{149}{720}\right) e(1115)e\left(\frac{11}{15}\right) e(91240)e\left(\frac{91}{240}\right) e(283360)e\left(\frac{283}{360}\right) e(157720)e\left(\frac{157}{720}\right) e(190)e\left(\frac{1}{90}\right) e(113240)e\left(\frac{113}{240}\right) e(97360)e\left(\frac{97}{360}\right)
χ259200(77,)\chi_{259200}(77,\cdot) 259200.bas 4320 yes 11 11 e(229432)e\left(\frac{229}{432}\right) e(5414320)e\left(\frac{541}{4320}\right) e(33594320)e\left(\frac{3359}{4320}\right) e(179360)e\left(\frac{179}{360}\right) e(13811440)e\left(\frac{1381}{1440}\right) e(432160)e\left(\frac{43}{2160}\right) e(5474320)e\left(\frac{547}{4320}\right) e(481540)e\left(\frac{481}{540}\right) e(3231440)e\left(\frac{323}{1440}\right) e(15672160)e\left(\frac{1567}{2160}\right)
χ259200(79,)\chi_{259200}(79,\cdot) 259200.yv 1080 no 1-1 11 e(59108)e\left(\frac{59}{108}\right) e(10431080)e\left(\frac{1043}{1080}\right) e(4571080)e\left(\frac{457}{1080}\right) e(4145)e\left(\frac{41}{45}\right) e(203360)e\left(\frac{203}{360}\right) e(29540)e\left(\frac{29}{540}\right) e(2811080)e\left(\frac{281}{1080}\right) e(181270)e\left(\frac{181}{270}\right) e(109360)e\left(\frac{109}{360}\right) e(341540)e\left(\frac{341}{540}\right)
χ259200(83,)\chi_{259200}(83,\cdot) 259200.bat 4320 yes 1-1 11 e(317432)e\left(\frac{317}{432}\right) e(31734320)e\left(\frac{3173}{4320}\right) e(12074320)e\left(\frac{1207}{4320}\right) e(247360)e\left(\frac{247}{360}\right) e(1731440)e\left(\frac{173}{1440}\right) e(8992160)e\left(\frac{899}{2160}\right) e(38514320)e\left(\frac{3851}{4320}\right) e(443540)e\left(\frac{443}{540}\right) e(8591440)e\left(\frac{859}{1440}\right) e(3112160)e\left(\frac{311}{2160}\right)
χ259200(89,)\chi_{259200}(89,\cdot) 259200.xo 720 no 1-1 11 e(172)e\left(\frac{1}{72}\right) e(241720)e\left(\frac{241}{720}\right) e(419720)e\left(\frac{419}{720}\right) e(2960)e\left(\frac{29}{60}\right) e(1240)e\left(\frac{1}{240}\right) e(283360)e\left(\frac{283}{360}\right) e(607720)e\left(\frac{607}{720}\right) e(190)e\left(\frac{1}{90}\right) e(23240)e\left(\frac{23}{240}\right) e(7360)e\left(\frac{7}{360}\right)
χ259200(91,)\chi_{259200}(91,\cdot) 259200.zi 1440 no 1-1 11 e(61144)e\left(\frac{61}{144}\right) e(12731440)e\left(\frac{1273}{1440}\right) e(1071440)e\left(\frac{107}{1440}\right) e(17120)e\left(\frac{17}{120}\right) e(193480)e\left(\frac{193}{480}\right) e(379720)e\left(\frac{379}{720}\right) e(13511440)e\left(\frac{1351}{1440}\right) e(43180)e\left(\frac{43}{180}\right) e(479480)e\left(\frac{479}{480}\right) e(571720)e\left(\frac{571}{720}\right)
χ259200(97,)\chi_{259200}(97,\cdot) 259200.xi 540 no 1-1 11 e(101108)e\left(\frac{101}{108}\right) e(439540)e\left(\frac{439}{540}\right) e(133270)e\left(\frac{133}{270}\right) e(89180)e\left(\frac{89}{180}\right) e(109180)e\left(\frac{109}{180}\right) e(359540)e\left(\frac{359}{540}\right) e(103540)e\left(\frac{103}{540}\right) e(38135)e\left(\frac{38}{135}\right) e(190)e\left(\frac{1}{90}\right) e(223270)e\left(\frac{223}{270}\right)
χ259200(101,)\chi_{259200}(101,\cdot) 259200.yn 864 no 1-1 11 e(95432)e\left(\frac{95}{432}\right) e(799864)e\left(\frac{799}{864}\right) e(797864)e\left(\frac{797}{864}\right) e(1172)e\left(\frac{11}{72}\right) e(199288)e\left(\frac{199}{288}\right) e(13432)e\left(\frac{13}{432}\right) e(625864)e\left(\frac{625}{864}\right) e(55108)e\left(\frac{55}{108}\right) e(137288)e\left(\frac{137}{288}\right) e(421432)e\left(\frac{421}{432}\right)
χ259200(103,)\chi_{259200}(103,\cdot) 259200.baf 2160 no 11 11 e(5216)e\left(\frac{5}{216}\right) e(16912160)e\left(\frac{1691}{2160}\right) e(14292160)e\left(\frac{1429}{2160}\right) e(7790)e\left(\frac{77}{90}\right) e(491720)e\left(\frac{491}{720}\right) e(831080)e\left(\frac{83}{1080}\right) e(21172160)e\left(\frac{2117}{2160}\right) e(133135)e\left(\frac{133}{135}\right) e(433720)e\left(\frac{433}{720}\right) e(171080)e\left(\frac{17}{1080}\right)
χ259200(107,)\chi_{259200}(107,\cdot) 259200.ok 96 no 1-1 11 e(2348)e\left(\frac{23}{48}\right) e(1996)e\left(\frac{19}{96}\right) e(1796)e\left(\frac{17}{96}\right) e(18)e\left(\frac{1}{8}\right) e(1132)e\left(\frac{11}{32}\right) e(3748)e\left(\frac{37}{48}\right) e(6196)e\left(\frac{61}{96}\right) e(112)e\left(\frac{1}{12}\right) e(1332)e\left(\frac{13}{32}\right) e(148)e\left(\frac{1}{48}\right)
χ259200(109,)\chi_{259200}(109,\cdot) 259200.we 480 no 11 11 e(148)e\left(\frac{1}{48}\right) e(301480)e\left(\frac{301}{480}\right) e(359480)e\left(\frac{359}{480}\right) e(940)e\left(\frac{9}{40}\right) e(21160)e\left(\frac{21}{160}\right) e(103240)e\left(\frac{103}{240}\right) e(67480)e\left(\frac{67}{480}\right) e(160)e\left(\frac{1}{60}\right) e(43160)e\left(\frac{43}{160}\right) e(7240)e\left(\frac{7}{240}\right)
χ259200(113,)\chi_{259200}(113,\cdot) 259200.ze 1080 no 11 11 e(1327)e\left(\frac{13}{27}\right) e(311080)e\left(\frac{31}{1080}\right) e(7191080)e\left(\frac{719}{1080}\right) e(163180)e\left(\frac{163}{180}\right) e(151360)e\left(\frac{151}{360}\right) e(59270)e\left(\frac{59}{270}\right) e(7571080)e\left(\frac{757}{1080}\right) e(61135)e\left(\frac{61}{135}\right) e(203360)e\left(\frac{203}{360}\right) e(247540)e\left(\frac{247}{540}\right)
χ259200(119,)\chi_{259200}(119,\cdot) 259200.bab 2160 no 11 11 e(85216)e\left(\frac{85}{216}\right) e(13692160)e\left(\frac{1369}{2160}\right) e(3712160)e\left(\frac{371}{2160}\right) e(161180)e\left(\frac{161}{180}\right) e(409720)e\left(\frac{409}{720}\right) e(71080)e\left(\frac{7}{1080}\right) e(9432160)e\left(\frac{943}{2160}\right) e(47135)e\left(\frac{47}{135}\right) e(647720)e\left(\frac{647}{720}\right) e(3431080)e\left(\frac{343}{1080}\right)
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