# Properties

 Modulus $8470$ Structure $$C_{660}\times C_{2}\times C_{2}$$ Order $2640$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8470)

pari: g = idealstar(,8470,2)

## Character group

 sage: G.order()  pari: g.no Order = 2640 sage: H.invariants()  pari: g.cyc Structure = $$C_{660}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8470}(6777,\cdot)$, $\chi_{8470}(6051,\cdot)$, $\chi_{8470}(7141,\cdot)$

## First 32 of 2640 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$37$$
$$\chi_{8470}(1,\cdot)$$ 8470.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8470}(3,\cdot)$$ 8470.cj 60 no $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{8470}(9,\cdot)$$ 8470.bw 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{8470}(13,\cdot)$$ 8470.de 220 no $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{107}{220}\right)$$ $$e\left(\frac{53}{220}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{69}{220}\right)$$
$$\chi_{8470}(17,\cdot)$$ 8470.dr 660 no $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{53}{220}\right)$$ $$e\left(\frac{161}{660}\right)$$ $$e\left(\frac{101}{330}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{157}{330}\right)$$ $$e\left(\frac{193}{660}\right)$$
$$\chi_{8470}(19,\cdot)$$ 8470.dl 330 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{101}{330}\right)$$ $$e\left(\frac{131}{165}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{239}{330}\right)$$ $$e\left(\frac{283}{330}\right)$$
$$\chi_{8470}(23,\cdot)$$ 8470.cz 132 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{61}{132}\right)$$ $$-i$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$
$$\chi_{8470}(27,\cdot)$$ 8470.bj 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{8470}(29,\cdot)$$ 8470.cw 110 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{109}{110}\right)$$
$$\chi_{8470}(31,\cdot)$$ 8470.di 330 no $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{157}{330}\right)$$ $$e\left(\frac{239}{330}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{133}{330}\right)$$ $$e\left(\frac{28}{165}\right)$$
$$\chi_{8470}(37,\cdot)$$ 8470.dq 660 no $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{69}{220}\right)$$ $$e\left(\frac{193}{660}\right)$$ $$e\left(\frac{283}{330}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{109}{110}\right)$$ $$e\left(\frac{28}{165}\right)$$ $$e\left(\frac{629}{660}\right)$$
$$\chi_{8470}(39,\cdot)$$ 8470.dk 330 no $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{59}{165}\right)$$ $$e\left(\frac{311}{330}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{71}{165}\right)$$ $$e\left(\frac{329}{330}\right)$$
$$\chi_{8470}(41,\cdot)$$ 8470.cx 110 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{34}{55}\right)$$ $$e\left(\frac{41}{55}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{53}{110}\right)$$ $$e\left(\frac{43}{55}\right)$$
$$\chi_{8470}(43,\cdot)$$ 8470.cb 44 no $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$-i$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$
$$\chi_{8470}(47,\cdot)$$ 8470.do 660 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{51}{220}\right)$$ $$e\left(\frac{487}{660}\right)$$ $$e\left(\frac{101}{165}\right)$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{71}{110}\right)$$ $$e\left(\frac{149}{330}\right)$$ $$e\left(\frac{221}{660}\right)$$
$$\chi_{8470}(51,\cdot)$$ 8470.dm 330 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{87}{110}\right)$$ $$e\left(\frac{119}{330}\right)$$ $$e\left(\frac{13}{330}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{73}{165}\right)$$ $$e\left(\frac{161}{165}\right)$$
$$\chi_{8470}(53,\cdot)$$ 8470.dq 660 no $$-1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{127}{220}\right)$$ $$e\left(\frac{419}{660}\right)$$ $$e\left(\frac{269}{330}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{97}{110}\right)$$ $$e\left(\frac{89}{165}\right)$$ $$e\left(\frac{367}{660}\right)$$
$$\chi_{8470}(57,\cdot)$$ 8470.dg 220 no $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{167}{220}\right)$$ $$e\left(\frac{93}{220}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{119}{220}\right)$$
$$\chi_{8470}(59,\cdot)$$ 8470.dn 330 no $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{152}{165}\right)$$ $$e\left(\frac{323}{330}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{52}{55}\right)$$ $$e\left(\frac{61}{330}\right)$$ $$e\left(\frac{17}{330}\right)$$
$$\chi_{8470}(61,\cdot)$$ 8470.dj 330 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{64}{165}\right)$$ $$e\left(\frac{68}{165}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{93}{110}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{47}{165}\right)$$
$$\chi_{8470}(67,\cdot)$$ 8470.cz 132 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{61}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$i$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{101}{132}\right)$$
$$\chi_{8470}(69,\cdot)$$ 8470.ct 110 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{79}{110}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{3}{110}\right)$$ $$e\left(\frac{91}{110}\right)$$
$$\chi_{8470}(71,\cdot)$$ 8470.cf 55 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{49}{55}\right)$$
$$\chi_{8470}(73,\cdot)$$ 8470.dr 660 no $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{159}{220}\right)$$ $$e\left(\frac{263}{660}\right)$$ $$e\left(\frac{83}{330}\right)$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{12}{55}\right)$$ $$e\left(\frac{31}{330}\right)$$ $$e\left(\frac{139}{660}\right)$$
$$\chi_{8470}(79,\cdot)$$ 8470.dk 330 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{16}{165}\right)$$ $$e\left(\frac{199}{330}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{37}{110}\right)$$ $$e\left(\frac{64}{165}\right)$$ $$e\left(\frac{271}{330}\right)$$
$$\chi_{8470}(81,\cdot)$$ 8470.bh 15 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{8470}(83,\cdot)$$ 8470.de 220 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{83}{220}\right)$$ $$e\left(\frac{37}{220}\right)$$ $$e\left(\frac{97}{110}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{54}{55}\right)$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{181}{220}\right)$$
$$\chi_{8470}(87,\cdot)$$ 8470.cy 132 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{119}{132}\right)$$ $$-i$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{89}{132}\right)$$
$$\chi_{8470}(89,\cdot)$$ 8470.ck 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{8470}(93,\cdot)$$ 8470.dq 660 no $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{220}\right)$$ $$e\left(\frac{391}{660}\right)$$ $$e\left(\frac{151}{330}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{61}{165}\right)$$ $$e\left(\frac{563}{660}\right)$$
$$\chi_{8470}(97,\cdot)$$ 8470.df 220 no $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{67}{220}\right)$$ $$e\left(\frac{173}{220}\right)$$ $$e\left(\frac{9}{55}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{110}\right)$$ $$e\left(\frac{71}{110}\right)$$ $$e\left(\frac{219}{220}\right)$$
$$\chi_{8470}(101,\cdot)$$ 8470.dj 330 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{86}{165}\right)$$ $$e\left(\frac{112}{165}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{193}{330}\right)$$ $$e\left(\frac{58}{165}\right)$$