# Properties

 Modulus $529984$ Structure $$C_{2}\times C_{2}\times C_{12}\times C_{4368}$$ Order $209664$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(529984)

pari: g = idealstar(,529984,2)

## Character group

 sage: G.order()  pari: g.no Order = 209664 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{12}\times C_{4368}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{529984}(380927,\cdot)$, $\chi_{529984}(298117,\cdot)$, $\chi_{529984}(324481,\cdot)$, $\chi_{529984}(28225,\cdot)$

## First 32 of 209664 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$27$$
$$\chi_{529984}(1,\cdot)$$ 529984.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{529984}(3,\cdot)$$ 529984.ccc 4368 yes $$1$$ $$1$$ $$e\left(\frac{947}{1456}\right)$$ $$e\left(\frac{139}{4368}\right)$$ $$e\left(\frac{219}{728}\right)$$ $$e\left(\frac{381}{1456}\right)$$ $$e\left(\frac{745}{1092}\right)$$ $$e\left(\frac{979}{1092}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{61}{168}\right)$$ $$e\left(\frac{139}{2184}\right)$$ $$e\left(\frac{1385}{1456}\right)$$
$$\chi_{529984}(5,\cdot)$$ 529984.cdi 4368 yes $$1$$ $$1$$ $$e\left(\frac{139}{4368}\right)$$ $$e\left(\frac{2645}{4368}\right)$$ $$e\left(\frac{139}{2184}\right)$$ $$e\left(\frac{3817}{4368}\right)$$ $$e\left(\frac{58}{91}\right)$$ $$e\left(\frac{475}{1092}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{103}{168}\right)$$ $$e\left(\frac{461}{2184}\right)$$ $$e\left(\frac{139}{1456}\right)$$
$$\chi_{529984}(9,\cdot)$$ 529984.car 2184 no $$1$$ $$1$$ $$e\left(\frac{219}{728}\right)$$ $$e\left(\frac{139}{2184}\right)$$ $$e\left(\frac{219}{364}\right)$$ $$e\left(\frac{381}{728}\right)$$ $$e\left(\frac{199}{546}\right)$$ $$e\left(\frac{433}{546}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{139}{1092}\right)$$ $$e\left(\frac{657}{728}\right)$$
$$\chi_{529984}(11,\cdot)$$ 529984.cbg 4368 yes $$1$$ $$1$$ $$e\left(\frac{381}{1456}\right)$$ $$e\left(\frac{3817}{4368}\right)$$ $$e\left(\frac{381}{728}\right)$$ $$e\left(\frac{239}{1456}\right)$$ $$e\left(\frac{37}{273}\right)$$ $$e\left(\frac{1045}{1092}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{151}{168}\right)$$ $$e\left(\frac{1633}{2184}\right)$$ $$e\left(\frac{1143}{1456}\right)$$
$$\chi_{529984}(15,\cdot)$$ 529984.bxd 1092 no $$1$$ $$1$$ $$e\left(\frac{745}{1092}\right)$$ $$e\left(\frac{58}{91}\right)$$ $$e\left(\frac{199}{546}\right)$$ $$e\left(\frac{37}{273}\right)$$ $$e\left(\frac{349}{1092}\right)$$ $$e\left(\frac{181}{546}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{25}{91}\right)$$ $$e\left(\frac{17}{364}\right)$$
$$\chi_{529984}(17,\cdot)$$ 529984.bwf 1092 no $$-1$$ $$1$$ $$e\left(\frac{979}{1092}\right)$$ $$e\left(\frac{475}{1092}\right)$$ $$e\left(\frac{433}{546}\right)$$ $$e\left(\frac{1045}{1092}\right)$$ $$e\left(\frac{181}{546}\right)$$ $$e\left(\frac{95}{182}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{475}{546}\right)$$ $$e\left(\frac{251}{364}\right)$$
$$\chi_{529984}(19,\cdot)$$ 529984.qq 48 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{529984}(23,\cdot)$$ 529984.bfr 168 no $$-1$$ $$1$$ $$e\left(\frac{61}{168}\right)$$ $$e\left(\frac{103}{168}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{151}{168}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{5}{56}\right)$$
$$\chi_{529984}(25,\cdot)$$ 529984.cax 2184 no $$1$$ $$1$$ $$e\left(\frac{139}{2184}\right)$$ $$e\left(\frac{461}{2184}\right)$$ $$e\left(\frac{139}{1092}\right)$$ $$e\left(\frac{1633}{2184}\right)$$ $$e\left(\frac{25}{91}\right)$$ $$e\left(\frac{475}{546}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{461}{1092}\right)$$ $$e\left(\frac{139}{728}\right)$$
$$\chi_{529984}(27,\cdot)$$ 529984.byh 1456 yes $$1$$ $$1$$ $$e\left(\frac{1385}{1456}\right)$$ $$e\left(\frac{139}{1456}\right)$$ $$e\left(\frac{657}{728}\right)$$ $$e\left(\frac{1143}{1456}\right)$$ $$e\left(\frac{17}{364}\right)$$ $$e\left(\frac{251}{364}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{56}\right)$$ $$e\left(\frac{139}{728}\right)$$ $$e\left(\frac{1243}{1456}\right)$$
$$\chi_{529984}(29,\cdot)$$ 529984.ccs 4368 yes $$1$$ $$1$$ $$e\left(\frac{1249}{4368}\right)$$ $$e\left(\frac{617}{1456}\right)$$ $$e\left(\frac{1249}{2184}\right)$$ $$e\left(\frac{4327}{4368}\right)$$ $$e\left(\frac{775}{1092}\right)$$ $$e\left(\frac{437}{1092}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{617}{728}\right)$$ $$e\left(\frac{1249}{1456}\right)$$
$$\chi_{529984}(31,\cdot)$$ 529984.bbv 156 no $$-1$$ $$1$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{529984}(33,\cdot)$$ 529984.bxs 1092 no $$1$$ $$1$$ $$e\left(\frac{83}{91}\right)$$ $$e\left(\frac{989}{1092}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{155}{364}\right)$$ $$e\left(\frac{893}{1092}\right)$$ $$e\left(\frac{233}{273}\right)$$ $$i$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{443}{546}\right)$$ $$e\left(\frac{67}{91}\right)$$
$$\chi_{529984}(37,\cdot)$$ 529984.cdd 4368 yes $$-1$$ $$1$$ $$e\left(\frac{2075}{4368}\right)$$ $$e\left(\frac{1613}{4368}\right)$$ $$e\left(\frac{2075}{2184}\right)$$ $$e\left(\frac{4313}{4368}\right)$$ $$e\left(\frac{461}{546}\right)$$ $$e\left(\frac{43}{364}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{1613}{2184}\right)$$ $$e\left(\frac{619}{1456}\right)$$
$$\chi_{529984}(41,\cdot)$$ 529984.cab 2184 no $$1$$ $$1$$ $$e\left(\frac{1193}{2184}\right)$$ $$e\left(\frac{99}{728}\right)$$ $$e\left(\frac{101}{1092}\right)$$ $$e\left(\frac{1709}{2184}\right)$$ $$e\left(\frac{745}{1092}\right)$$ $$e\left(\frac{535}{546}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{99}{364}\right)$$ $$e\left(\frac{465}{728}\right)$$
$$\chi_{529984}(43,\cdot)$$ 529984.ccq 4368 yes $$-1$$ $$1$$ $$e\left(\frac{239}{4368}\right)$$ $$e\left(\frac{1447}{1456}\right)$$ $$e\left(\frac{239}{2184}\right)$$ $$e\left(\frac{3617}{4368}\right)$$ $$e\left(\frac{53}{1092}\right)$$ $$e\left(\frac{547}{1092}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{163}{168}\right)$$ $$e\left(\frac{719}{728}\right)$$ $$e\left(\frac{239}{1456}\right)$$
$$\chi_{529984}(45,\cdot)$$ 529984.ccz 4368 yes $$1$$ $$1$$ $$e\left(\frac{1453}{4368}\right)$$ $$e\left(\frac{2923}{4368}\right)$$ $$e\left(\frac{1453}{2184}\right)$$ $$e\left(\frac{1735}{4368}\right)$$ $$e\left(\frac{1}{546}\right)$$ $$e\left(\frac{83}{364}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{739}{2184}\right)$$ $$e\left(\frac{1453}{1456}\right)$$
$$\chi_{529984}(47,\cdot)$$ 529984.bwv 1092 no $$-1$$ $$1$$ $$e\left(\frac{1033}{1092}\right)$$ $$e\left(\frac{457}{546}\right)$$ $$e\left(\frac{487}{546}\right)$$ $$e\left(\frac{166}{273}\right)$$ $$e\left(\frac{285}{364}\right)$$ $$e\left(\frac{256}{273}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{184}{273}\right)$$ $$e\left(\frac{305}{364}\right)$$
$$\chi_{529984}(51,\cdot)$$ 529984.cbv 4368 yes $$-1$$ $$1$$ $$e\left(\frac{2389}{4368}\right)$$ $$e\left(\frac{2039}{4368}\right)$$ $$e\left(\frac{205}{2184}\right)$$ $$e\left(\frac{955}{4368}\right)$$ $$e\left(\frac{5}{364}\right)$$ $$e\left(\frac{457}{1092}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{25}{168}\right)$$ $$e\left(\frac{2039}{2184}\right)$$ $$e\left(\frac{933}{1456}\right)$$
$$\chi_{529984}(53,\cdot)$$ 529984.ccb 4368 yes $$1$$ $$1$$ $$e\left(\frac{2447}{4368}\right)$$ $$e\left(\frac{613}{4368}\right)$$ $$e\left(\frac{263}{2184}\right)$$ $$e\left(\frac{1385}{4368}\right)$$ $$e\left(\frac{255}{364}\right)$$ $$e\left(\frac{11}{1092}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{71}{168}\right)$$ $$e\left(\frac{613}{2184}\right)$$ $$e\left(\frac{991}{1456}\right)$$
$$\chi_{529984}(55,\cdot)$$ 529984.byt 2184 no $$1$$ $$1$$ $$e\left(\frac{641}{2184}\right)$$ $$e\left(\frac{349}{728}\right)$$ $$e\left(\frac{641}{1092}\right)$$ $$e\left(\frac{83}{2184}\right)$$ $$e\left(\frac{211}{273}\right)$$ $$e\left(\frac{107}{273}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{349}{364}\right)$$ $$e\left(\frac{641}{728}\right)$$
$$\chi_{529984}(57,\cdot)$$ 529984.btx 728 no $$-1$$ $$1$$ $$e\left(\frac{701}{728}\right)$$ $$e\left(\frac{281}{728}\right)$$ $$e\left(\frac{337}{364}\right)$$ $$e\left(\frac{145}{728}\right)$$ $$e\left(\frac{127}{364}\right)$$ $$e\left(\frac{74}{91}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{281}{364}\right)$$ $$e\left(\frac{647}{728}\right)$$
$$\chi_{529984}(59,\cdot)$$ 529984.cbi 4368 yes $$-1$$ $$1$$ $$e\left(\frac{3571}{4368}\right)$$ $$e\left(\frac{253}{4368}\right)$$ $$e\left(\frac{1387}{2184}\right)$$ $$e\left(\frac{1321}{4368}\right)$$ $$e\left(\frac{239}{273}\right)$$ $$e\left(\frac{89}{364}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{17}{56}\right)$$ $$e\left(\frac{253}{2184}\right)$$ $$e\left(\frac{659}{1456}\right)$$
$$\chi_{529984}(61,\cdot)$$ 529984.cco 4368 yes $$-1$$ $$1$$ $$e\left(\frac{155}{1456}\right)$$ $$e\left(\frac{3755}{4368}\right)$$ $$e\left(\frac{155}{728}\right)$$ $$e\left(\frac{1237}{1456}\right)$$ $$e\left(\frac{1055}{1092}\right)$$ $$e\left(\frac{899}{1092}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{1571}{2184}\right)$$ $$e\left(\frac{465}{1456}\right)$$
$$\chi_{529984}(67,\cdot)$$ 529984.btf 624 no $$1$$ $$1$$ $$e\left(\frac{29}{208}\right)$$ $$e\left(\frac{409}{624}\right)$$ $$e\left(\frac{29}{104}\right)$$ $$e\left(\frac{111}{208}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{97}{312}\right)$$ $$e\left(\frac{87}{208}\right)$$
$$\chi_{529984}(69,\cdot)$$ 529984.cct 4368 yes $$-1$$ $$1$$ $$e\left(\frac{59}{4368}\right)$$ $$e\left(\frac{939}{1456}\right)$$ $$e\left(\frac{59}{2184}\right)$$ $$e\left(\frac{701}{4368}\right)$$ $$e\left(\frac{719}{1092}\right)$$ $$e\left(\frac{745}{1092}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{139}{168}\right)$$ $$e\left(\frac{211}{728}\right)$$ $$e\left(\frac{59}{1456}\right)$$
$$\chi_{529984}(71,\cdot)$$ 529984.bzp 2184 no $$1$$ $$1$$ $$e\left(\frac{1843}{2184}\right)$$ $$e\left(\frac{73}{728}\right)$$ $$e\left(\frac{751}{1092}\right)$$ $$e\left(\frac{2047}{2184}\right)$$ $$e\left(\frac{1031}{1092}\right)$$ $$e\left(\frac{1}{273}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{73}{364}\right)$$ $$e\left(\frac{387}{728}\right)$$
$$\chi_{529984}(73,\cdot)$$ 529984.cad 2184 no $$1$$ $$1$$ $$e\left(\frac{1189}{2184}\right)$$ $$e\left(\frac{1889}{2184}\right)$$ $$e\left(\frac{97}{1092}\right)$$ $$e\left(\frac{1717}{2184}\right)$$ $$e\left(\frac{149}{364}\right)$$ $$e\left(\frac{139}{546}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{797}{1092}\right)$$ $$e\left(\frac{461}{728}\right)$$
$$\chi_{529984}(75,\cdot)$$ 529984.ccm 4368 yes $$1$$ $$1$$ $$e\left(\frac{3119}{4368}\right)$$ $$e\left(\frac{1061}{4368}\right)$$ $$e\left(\frac{935}{2184}\right)$$ $$e\left(\frac{41}{4368}\right)$$ $$e\left(\frac{1045}{1092}\right)$$ $$e\left(\frac{279}{364}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{1061}{2184}\right)$$ $$e\left(\frac{207}{1456}\right)$$
$$\chi_{529984}(79,\cdot)$$ 529984.bdn 156 no $$-1$$ $$1$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{51}{52}\right)$$
$$\chi_{529984}(81,\cdot)$$ 529984.bvk 1092 no $$1$$ $$1$$ $$e\left(\frac{219}{364}\right)$$ $$e\left(\frac{139}{1092}\right)$$ $$e\left(\frac{37}{182}\right)$$ $$e\left(\frac{17}{364}\right)$$ $$e\left(\frac{199}{273}\right)$$ $$e\left(\frac{160}{273}\right)$$ $$i$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{139}{546}\right)$$ $$e\left(\frac{293}{364}\right)$$