# Properties

 Modulus $85600$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{2120}$$ Order $33920$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(85600)

pari: g = idealstar(,85600,2)

## Character group

 sage: G.order()  pari: g.no Order = 33920 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{2120}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{85600}(26751,\cdot)$, $\chi_{85600}(32101,\cdot)$, $\chi_{85600}(82177,\cdot)$, $\chi_{85600}(16801,\cdot)$

## First 32 of 33920 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{85600}(1,\cdot)$$ 85600.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{85600}(3,\cdot)$$ 85600.ic 2120 yes $$1$$ $$1$$ $$e\left(\frac{639}{2120}\right)$$ $$e\left(\frac{21}{53}\right)$$ $$e\left(\frac{639}{1060}\right)$$ $$e\left(\frac{1067}{2120}\right)$$ $$e\left(\frac{1103}{2120}\right)$$ $$e\left(\frac{213}{1060}\right)$$ $$e\left(\frac{1981}{2120}\right)$$ $$e\left(\frac{1479}{2120}\right)$$ $$e\left(\frac{144}{265}\right)$$ $$e\left(\frac{1917}{2120}\right)$$
$$\chi_{85600}(7,\cdot)$$ 85600.fa 212 no $$-1$$ $$1$$ $$e\left(\frac{21}{53}\right)$$ $$e\left(\frac{147}{212}\right)$$ $$e\left(\frac{42}{53}\right)$$ $$e\left(\frac{143}{212}\right)$$ $$e\left(\frac{19}{106}\right)$$ $$e\left(\frac{3}{212}\right)$$ $$e\left(\frac{83}{212}\right)$$ $$e\left(\frac{19}{212}\right)$$ $$e\left(\frac{191}{212}\right)$$ $$e\left(\frac{10}{53}\right)$$
$$\chi_{85600}(9,\cdot)$$ 85600.hh 1060 no $$1$$ $$1$$ $$e\left(\frac{639}{1060}\right)$$ $$e\left(\frac{42}{53}\right)$$ $$e\left(\frac{109}{530}\right)$$ $$e\left(\frac{7}{1060}\right)$$ $$e\left(\frac{43}{1060}\right)$$ $$e\left(\frac{213}{530}\right)$$ $$e\left(\frac{921}{1060}\right)$$ $$e\left(\frac{419}{1060}\right)$$ $$e\left(\frac{23}{265}\right)$$ $$e\left(\frac{857}{1060}\right)$$
$$\chi_{85600}(11,\cdot)$$ 85600.if 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1067}{2120}\right)$$ $$e\left(\frac{143}{212}\right)$$ $$e\left(\frac{7}{1060}\right)$$ $$e\left(\frac{2101}{2120}\right)$$ $$e\left(\frac{1019}{2120}\right)$$ $$e\left(\frac{487}{530}\right)$$ $$e\left(\frac{983}{2120}\right)$$ $$e\left(\frac{377}{2120}\right)$$ $$e\left(\frac{973}{1060}\right)$$ $$e\left(\frac{1081}{2120}\right)$$
$$\chi_{85600}(13,\cdot)$$ 85600.in 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1103}{2120}\right)$$ $$e\left(\frac{19}{106}\right)$$ $$e\left(\frac{43}{1060}\right)$$ $$e\left(\frac{1019}{2120}\right)$$ $$e\left(\frac{51}{2120}\right)$$ $$e\left(\frac{721}{1060}\right)$$ $$e\left(\frac{1117}{2120}\right)$$ $$e\left(\frac{1483}{2120}\right)$$ $$e\left(\frac{471}{530}\right)$$ $$e\left(\frac{1189}{2120}\right)$$
$$\chi_{85600}(17,\cdot)$$ 85600.hn 1060 no $$1$$ $$1$$ $$e\left(\frac{213}{1060}\right)$$ $$e\left(\frac{3}{212}\right)$$ $$e\left(\frac{213}{530}\right)$$ $$e\left(\frac{487}{530}\right)$$ $$e\left(\frac{721}{1060}\right)$$ $$e\left(\frac{407}{1060}\right)$$ $$e\left(\frac{143}{265}\right)$$ $$e\left(\frac{57}{265}\right)$$ $$e\left(\frac{119}{1060}\right)$$ $$e\left(\frac{639}{1060}\right)$$
$$\chi_{85600}(19,\cdot)$$ 85600.ii 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1981}{2120}\right)$$ $$e\left(\frac{83}{212}\right)$$ $$e\left(\frac{921}{1060}\right)$$ $$e\left(\frac{983}{2120}\right)$$ $$e\left(\frac{1117}{2120}\right)$$ $$e\left(\frac{143}{265}\right)$$ $$e\left(\frac{469}{2120}\right)$$ $$e\left(\frac{691}{2120}\right)$$ $$e\left(\frac{289}{1060}\right)$$ $$e\left(\frac{1703}{2120}\right)$$
$$\chi_{85600}(21,\cdot)$$ 85600.ij 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1479}{2120}\right)$$ $$e\left(\frac{19}{212}\right)$$ $$e\left(\frac{419}{1060}\right)$$ $$e\left(\frac{377}{2120}\right)$$ $$e\left(\frac{1483}{2120}\right)$$ $$e\left(\frac{57}{265}\right)$$ $$e\left(\frac{691}{2120}\right)$$ $$e\left(\frac{1669}{2120}\right)$$ $$e\left(\frac{471}{1060}\right)$$ $$e\left(\frac{197}{2120}\right)$$
$$\chi_{85600}(23,\cdot)$$ 85600.hw 1060 no $$1$$ $$1$$ $$e\left(\frac{144}{265}\right)$$ $$e\left(\frac{191}{212}\right)$$ $$e\left(\frac{23}{265}\right)$$ $$e\left(\frac{973}{1060}\right)$$ $$e\left(\frac{471}{530}\right)$$ $$e\left(\frac{119}{1060}\right)$$ $$e\left(\frac{289}{1060}\right)$$ $$e\left(\frac{471}{1060}\right)$$ $$e\left(\frac{333}{1060}\right)$$ $$e\left(\frac{167}{265}\right)$$
$$\chi_{85600}(27,\cdot)$$ 85600.ic 2120 yes $$1$$ $$1$$ $$e\left(\frac{1917}{2120}\right)$$ $$e\left(\frac{10}{53}\right)$$ $$e\left(\frac{857}{1060}\right)$$ $$e\left(\frac{1081}{2120}\right)$$ $$e\left(\frac{1189}{2120}\right)$$ $$e\left(\frac{639}{1060}\right)$$ $$e\left(\frac{1703}{2120}\right)$$ $$e\left(\frac{197}{2120}\right)$$ $$e\left(\frac{167}{265}\right)$$ $$e\left(\frac{1511}{2120}\right)$$
$$\chi_{85600}(29,\cdot)$$ 85600.ik 2120 yes $$1$$ $$1$$ $$e\left(\frac{2029}{2120}\right)$$ $$e\left(\frac{49}{212}\right)$$ $$e\left(\frac{969}{1060}\right)$$ $$e\left(\frac{247}{2120}\right)$$ $$e\left(\frac{1593}{2120}\right)$$ $$e\left(\frac{147}{265}\right)$$ $$e\left(\frac{2061}{2120}\right)$$ $$e\left(\frac{399}{2120}\right)$$ $$e\left(\frac{71}{1060}\right)$$ $$e\left(\frac{1847}{2120}\right)$$
$$\chi_{85600}(31,\cdot)$$ 85600.go 530 no $$1$$ $$1$$ $$e\left(\frac{69}{530}\right)$$ $$e\left(\frac{24}{53}\right)$$ $$e\left(\frac{69}{265}\right)$$ $$e\left(\frac{267}{530}\right)$$ $$e\left(\frac{44}{265}\right)$$ $$e\left(\frac{311}{530}\right)$$ $$e\left(\frac{301}{530}\right)$$ $$e\left(\frac{309}{530}\right)$$ $$e\left(\frac{367}{530}\right)$$ $$e\left(\frac{207}{530}\right)$$
$$\chi_{85600}(33,\cdot)$$ 85600.hq 1060 no $$-1$$ $$1$$ $$e\left(\frac{853}{1060}\right)$$ $$e\left(\frac{15}{212}\right)$$ $$e\left(\frac{323}{530}\right)$$ $$e\left(\frac{131}{265}\right)$$ $$e\left(\frac{1}{1060}\right)$$ $$e\left(\frac{127}{1060}\right)$$ $$e\left(\frac{211}{530}\right)$$ $$e\left(\frac{232}{265}\right)$$ $$e\left(\frac{489}{1060}\right)$$ $$e\left(\frac{439}{1060}\right)$$
$$\chi_{85600}(37,\cdot)$$ 85600.in 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1313}{2120}\right)$$ $$e\left(\frac{97}{106}\right)$$ $$e\left(\frac{253}{1060}\right)$$ $$e\left(\frac{1509}{2120}\right)$$ $$e\left(\frac{941}{2120}\right)$$ $$e\left(\frac{791}{1060}\right)$$ $$e\left(\frac{1987}{2120}\right)$$ $$e\left(\frac{1133}{2120}\right)$$ $$e\left(\frac{491}{530}\right)$$ $$e\left(\frac{1819}{2120}\right)$$
$$\chi_{85600}(39,\cdot)$$ 85600.hs 1060 no $$-1$$ $$1$$ $$e\left(\frac{871}{1060}\right)$$ $$e\left(\frac{61}{106}\right)$$ $$e\left(\frac{341}{530}\right)$$ $$e\left(\frac{1043}{1060}\right)$$ $$e\left(\frac{577}{1060}\right)$$ $$e\left(\frac{467}{530}\right)$$ $$e\left(\frac{489}{1060}\right)$$ $$e\left(\frac{421}{1060}\right)$$ $$e\left(\frac{229}{530}\right)$$ $$e\left(\frac{493}{1060}\right)$$
$$\chi_{85600}(41,\cdot)$$ 85600.hu 1060 no $$1$$ $$1$$ $$e\left(\frac{69}{1060}\right)$$ $$e\left(\frac{77}{106}\right)$$ $$e\left(\frac{69}{530}\right)$$ $$e\left(\frac{267}{1060}\right)$$ $$e\left(\frac{353}{1060}\right)$$ $$e\left(\frac{144}{265}\right)$$ $$e\left(\frac{301}{1060}\right)$$ $$e\left(\frac{839}{1060}\right)$$ $$e\left(\frac{51}{530}\right)$$ $$e\left(\frac{207}{1060}\right)$$
$$\chi_{85600}(43,\cdot)$$ 85600.fz 424 no $$-1$$ $$1$$ $$e\left(\frac{249}{424}\right)$$ $$e\left(\frac{23}{53}\right)$$ $$e\left(\frac{37}{212}\right)$$ $$e\left(\frac{369}{424}\right)$$ $$e\left(\frac{177}{424}\right)$$ $$e\left(\frac{83}{212}\right)$$ $$e\left(\frac{335}{424}\right)$$ $$e\left(\frac{9}{424}\right)$$ $$e\left(\frac{1}{106}\right)$$ $$e\left(\frac{323}{424}\right)$$
$$\chi_{85600}(47,\cdot)$$ 85600.hp 1060 no $$1$$ $$1$$ $$e\left(\frac{567}{1060}\right)$$ $$e\left(\frac{111}{212}\right)$$ $$e\left(\frac{37}{530}\right)$$ $$e\left(\frac{79}{265}\right)$$ $$e\left(\frac{389}{1060}\right)$$ $$e\left(\frac{113}{1060}\right)$$ $$e\left(\frac{459}{530}\right)$$ $$e\left(\frac{31}{530}\right)$$ $$e\left(\frac{481}{1060}\right)$$ $$e\left(\frac{641}{1060}\right)$$
$$\chi_{85600}(49,\cdot)$$ 85600.eo 106 no $$1$$ $$1$$ $$e\left(\frac{42}{53}\right)$$ $$e\left(\frac{41}{106}\right)$$ $$e\left(\frac{31}{53}\right)$$ $$e\left(\frac{37}{106}\right)$$ $$e\left(\frac{19}{53}\right)$$ $$e\left(\frac{3}{106}\right)$$ $$e\left(\frac{83}{106}\right)$$ $$e\left(\frac{19}{106}\right)$$ $$e\left(\frac{85}{106}\right)$$ $$e\left(\frac{20}{53}\right)$$
$$\chi_{85600}(51,\cdot)$$ 85600.gb 424 no $$1$$ $$1$$ $$e\left(\frac{213}{424}\right)$$ $$e\left(\frac{87}{212}\right)$$ $$e\left(\frac{1}{212}\right)$$ $$e\left(\frac{179}{424}\right)$$ $$e\left(\frac{85}{424}\right)$$ $$e\left(\frac{31}{53}\right)$$ $$e\left(\frac{201}{424}\right)$$ $$e\left(\frac{387}{424}\right)$$ $$e\left(\frac{139}{212}\right)$$ $$e\left(\frac{215}{424}\right)$$
$$\chi_{85600}(53,\cdot)$$ 85600.id 2120 yes $$-1$$ $$1$$ $$e\left(\frac{1409}{2120}\right)$$ $$e\left(\frac{5}{53}\right)$$ $$e\left(\frac{349}{1060}\right)$$ $$e\left(\frac{1097}{2120}\right)$$ $$e\left(\frac{1893}{2120}\right)$$ $$e\left(\frac{293}{1060}\right)$$ $$e\left(\frac{1991}{2120}\right)$$ $$e\left(\frac{1609}{2120}\right)$$ $$e\left(\frac{4}{265}\right)$$ $$e\left(\frac{2107}{2120}\right)$$
$$\chi_{85600}(57,\cdot)$$ 85600.fu 212 no $$-1$$ $$1$$ $$e\left(\frac{25}{106}\right)$$ $$e\left(\frac{167}{212}\right)$$ $$e\left(\frac{25}{53}\right)$$ $$e\left(\frac{205}{212}\right)$$ $$e\left(\frac{5}{106}\right)$$ $$e\left(\frac{157}{212}\right)$$ $$e\left(\frac{33}{212}\right)$$ $$e\left(\frac{5}{212}\right)$$ $$e\left(\frac{173}{212}\right)$$ $$e\left(\frac{75}{106}\right)$$
$$\chi_{85600}(59,\cdot)$$ 85600.ig 2120 yes $$1$$ $$1$$ $$e\left(\frac{1363}{2120}\right)$$ $$e\left(\frac{163}{212}\right)$$ $$e\left(\frac{303}{1060}\right)$$ $$e\left(\frac{1449}{2120}\right)$$ $$e\left(\frac{2011}{2120}\right)$$ $$e\left(\frac{183}{530}\right)$$ $$e\left(\frac{907}{2120}\right)$$ $$e\left(\frac{873}{2120}\right)$$ $$e\left(\frac{247}{1060}\right)$$ $$e\left(\frac{1969}{2120}\right)$$
$$\chi_{85600}(61,\cdot)$$ 85600.ih 2120 yes $$1$$ $$1$$ $$e\left(\frac{697}{2120}\right)$$ $$e\left(\frac{171}{212}\right)$$ $$e\left(\frac{697}{1060}\right)$$ $$e\left(\frac{1591}{2120}\right)$$ $$e\left(\frac{309}{2120}\right)$$ $$e\left(\frac{337}{530}\right)$$ $$e\left(\frac{813}{2120}\right)$$ $$e\left(\frac{287}{2120}\right)$$ $$e\left(\frac{953}{1060}\right)$$ $$e\left(\frac{2091}{2120}\right)$$
$$\chi_{85600}(63,\cdot)$$ 85600.hk 1060 no $$-1$$ $$1$$ $$e\left(\frac{1059}{1060}\right)$$ $$e\left(\frac{103}{212}\right)$$ $$e\left(\frac{529}{530}\right)$$ $$e\left(\frac{361}{530}\right)$$ $$e\left(\frac{233}{1060}\right)$$ $$e\left(\frac{441}{1060}\right)$$ $$e\left(\frac{69}{265}\right)$$ $$e\left(\frac{257}{530}\right)$$ $$e\left(\frac{1047}{1060}\right)$$ $$e\left(\frac{1057}{1060}\right)$$
$$\chi_{85600}(67,\cdot)$$ 85600.ib 2120 yes $$-1$$ $$1$$ $$e\left(\frac{411}{2120}\right)$$ $$e\left(\frac{15}{53}\right)$$ $$e\left(\frac{411}{1060}\right)$$ $$e\left(\frac{323}{2120}\right)$$ $$e\left(\frac{1227}{2120}\right)$$ $$e\left(\frac{137}{1060}\right)$$ $$e\left(\frac{1309}{2120}\right)$$ $$e\left(\frac{1011}{2120}\right)$$ $$e\left(\frac{77}{530}\right)$$ $$e\left(\frac{1233}{2120}\right)$$
$$\chi_{85600}(69,\cdot)$$ 85600.ik 2120 yes $$1$$ $$1$$ $$e\left(\frac{1791}{2120}\right)$$ $$e\left(\frac{63}{212}\right)$$ $$e\left(\frac{731}{1060}\right)$$ $$e\left(\frac{893}{2120}\right)$$ $$e\left(\frac{867}{2120}\right)$$ $$e\left(\frac{83}{265}\right)$$ $$e\left(\frac{439}{2120}\right)$$ $$e\left(\frac{301}{2120}\right)$$ $$e\left(\frac{909}{1060}\right)$$ $$e\left(\frac{1133}{2120}\right)$$
$$\chi_{85600}(71,\cdot)$$ 85600.ht 1060 no $$1$$ $$1$$ $$e\left(\frac{237}{1060}\right)$$ $$e\left(\frac{11}{106}\right)$$ $$e\left(\frac{237}{530}\right)$$ $$e\left(\frac{871}{1060}\right)$$ $$e\left(\frac{959}{1060}\right)$$ $$e\left(\frac{79}{530}\right)$$ $$e\left(\frac{573}{1060}\right)$$ $$e\left(\frac{347}{1060}\right)$$ $$e\left(\frac{174}{265}\right)$$ $$e\left(\frac{711}{1060}\right)$$
$$\chi_{85600}(73,\cdot)$$ 85600.hc 1060 no $$1$$ $$1$$ $$e\left(\frac{483}{530}\right)$$ $$e\left(\frac{195}{212}\right)$$ $$e\left(\frac{218}{265}\right)$$ $$e\left(\frac{823}{1060}\right)$$ $$e\left(\frac{351}{530}\right)$$ $$e\left(\frac{909}{1060}\right)$$ $$e\left(\frac{239}{1060}\right)$$ $$e\left(\frac{881}{1060}\right)$$ $$e\left(\frac{103}{1060}\right)$$ $$e\left(\frac{389}{530}\right)$$
$$\chi_{85600}(77,\cdot)$$ 85600.io 2120 yes $$1$$ $$1$$ $$e\left(\frac{1907}{2120}\right)$$ $$e\left(\frac{39}{106}\right)$$ $$e\left(\frac{847}{1060}\right)$$ $$e\left(\frac{1411}{2120}\right)$$ $$e\left(\frac{1399}{2120}\right)$$ $$e\left(\frac{989}{1060}\right)$$ $$e\left(\frac{1813}{2120}\right)$$ $$e\left(\frac{567}{2120}\right)$$ $$e\left(\frac{217}{265}\right)$$ $$e\left(\frac{1481}{2120}\right)$$
$$\chi_{85600}(79,\cdot)$$ 85600.gq 530 no $$-1$$ $$1$$ $$e\left(\frac{221}{530}\right)$$ $$e\left(\frac{40}{53}\right)$$ $$e\left(\frac{221}{265}\right)$$ $$e\left(\frac{249}{265}\right)$$ $$e\left(\frac{91}{265}\right)$$ $$e\left(\frac{59}{530}\right)$$ $$e\left(\frac{242}{265}\right)$$ $$e\left(\frac{91}{530}\right)$$ $$e\left(\frac{244}{265}\right)$$ $$e\left(\frac{133}{530}\right)$$