# Properties

 Modulus 4730 Structure $$C_{420}\times C_{2}\times C_{2}$$ Order 1680

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(4730)

pari: g = idealstar(,4730,2)

## Character group

 sage: G.order()  pari: g.no Order = 1680 sage: H.invariants()  pari: g.cyc Structure = $$C_{420}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4730}(1293,\cdot)$, $\chi_{4730}(3871,\cdot)$, $\chi_{4730}(2751,\cdot)$

## First 32 of 1680 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.

orbit label order primitive -1 1 3 7 9 13 17 19 21 23 27 29
$$\chi_{4730}(1,\cdot)$$ 4730.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4730}(3,\cdot)$$ 4730.do 420 no $$1$$ $$1$$ $$e\left(\frac{283}{420}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{341}{420}\right)$$ $$e\left(\frac{359}{420}\right)$$ $$e\left(\frac{37}{105}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{3}{140}\right)$$ $$e\left(\frac{8}{105}\right)$$
$$\chi_{4730}(7,\cdot)$$ 4730.cn 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{4730}(9,\cdot)$$ 4730.dl 210 no $$1$$ $$1$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{149}{210}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{3}{70}\right)$$ $$e\left(\frac{16}{105}\right)$$
$$\chi_{4730}(13,\cdot)$$ 4730.dp 420 no $$1$$ $$1$$ $$e\left(\frac{341}{420}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{307}{420}\right)$$ $$e\left(\frac{253}{420}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{61}{140}\right)$$ $$e\left(\frac{46}{105}\right)$$
$$\chi_{4730}(17,\cdot)$$ 4730.dp 420 no $$1$$ $$1$$ $$e\left(\frac{359}{420}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{149}{210}\right)$$ $$e\left(\frac{253}{420}\right)$$ $$e\left(\frac{307}{420}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{79}{140}\right)$$ $$e\left(\frac{94}{105}\right)$$
$$\chi_{4730}(19,\cdot)$$ 4730.dh 210 no $$1$$ $$1$$ $$e\left(\frac{37}{105}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{68}{105}\right)$$
$$\chi_{4730}(21,\cdot)$$ 4730.bi 14 no $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$-1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{4730}(23,\cdot)$$ 4730.cy 84 no $$-1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{42}\right)$$
$$\chi_{4730}(27,\cdot)$$ 4730.df 140 no $$1$$ $$1$$ $$e\left(\frac{3}{140}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{70}\right)$$ $$e\left(\frac{61}{140}\right)$$ $$e\left(\frac{79}{140}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{9}{140}\right)$$ $$e\left(\frac{8}{35}\right)$$
$$\chi_{4730}(29,\cdot)$$ 4730.dh 210 no $$1$$ $$1$$ $$e\left(\frac{8}{105}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{46}{105}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{97}{105}\right)$$
$$\chi_{4730}(31,\cdot)$$ 4730.dc 105 no $$1$$ $$1$$ $$e\left(\frac{64}{105}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{17}{105}\right)$$ $$e\left(\frac{19}{105}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{41}{105}\right)$$
$$\chi_{4730}(37,\cdot)$$ 4730.cq 60 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{4730}(39,\cdot)$$ 4730.cx 70 no $$1$$ $$1$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$
$$\chi_{4730}(41,\cdot)$$ 4730.cw 70 no $$-1$$ $$1$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{43}{70}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{67}{70}\right)$$
$$\chi_{4730}(47,\cdot)$$ 4730.dd 140 no $$-1$$ $$1$$ $$e\left(\frac{61}{140}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{97}{140}\right)$$ $$e\left(\frac{43}{140}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{43}{140}\right)$$ $$e\left(\frac{57}{70}\right)$$
$$\chi_{4730}(49,\cdot)$$ 4730.by 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{4730}(51,\cdot)$$ 4730.cr 70 no $$1$$ $$1$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{34}{35}\right)$$
$$\chi_{4730}(53,\cdot)$$ 4730.dq 420 no $$-1$$ $$1$$ $$e\left(\frac{121}{420}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{121}{210}\right)$$ $$e\left(\frac{197}{420}\right)$$ $$e\left(\frac{83}{420}\right)$$ $$e\left(\frac{173}{210}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{121}{140}\right)$$ $$e\left(\frac{97}{210}\right)$$
$$\chi_{4730}(57,\cdot)$$ 4730.dp 420 no $$1$$ $$1$$ $$e\left(\frac{11}{420}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{210}\right)$$ $$e\left(\frac{37}{420}\right)$$ $$e\left(\frac{103}{420}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{11}{140}\right)$$ $$e\left(\frac{76}{105}\right)$$
$$\chi_{4730}(59,\cdot)$$ 4730.ct 70 no $$1$$ $$1$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{69}{70}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{29}{35}\right)$$
$$\chi_{4730}(61,\cdot)$$ 4730.dn 210 no $$1$$ $$1$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{209}{210}\right)$$ $$e\left(\frac{71}{210}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{64}{105}\right)$$
$$\chi_{4730}(63,\cdot)$$ 4730.dr 420 no $$-1$$ $$1$$ $$e\left(\frac{223}{420}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{210}\right)$$ $$e\left(\frac{311}{420}\right)$$ $$e\left(\frac{389}{420}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{83}{140}\right)$$ $$e\left(\frac{151}{210}\right)$$
$$\chi_{4730}(67,\cdot)$$ 4730.cy 84 no $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$
$$\chi_{4730}(69,\cdot)$$ 4730.dj 210 no $$-1$$ $$1$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{64}{105}\right)$$ $$e\left(\frac{53}{210}\right)$$ $$e\left(\frac{17}{210}\right)$$ $$e\left(\frac{19}{210}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{32}{35}\right)$$ $$e\left(\frac{41}{210}\right)$$
$$\chi_{4730}(71,\cdot)$$ 4730.dk 210 no $$-1$$ $$1$$ $$e\left(\frac{67}{210}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{67}{105}\right)$$ $$e\left(\frac{22}{105}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{97}{210}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{67}{70}\right)$$ $$e\left(\frac{143}{210}\right)$$
$$\chi_{4730}(73,\cdot)$$ 4730.dr 420 no $$-1$$ $$1$$ $$e\left(\frac{47}{420}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{47}{210}\right)$$ $$e\left(\frac{139}{420}\right)$$ $$e\left(\frac{1}{420}\right)$$ $$e\left(\frac{121}{210}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{47}{140}\right)$$ $$e\left(\frac{29}{210}\right)$$
$$\chi_{4730}(79,\cdot)$$ 4730.cb 30 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{4730}(81,\cdot)$$ 4730.dc 105 no $$1$$ $$1$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{44}{105}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{32}{105}\right)$$
$$\chi_{4730}(83,\cdot)$$ 4730.dp 420 no $$1$$ $$1$$ $$e\left(\frac{409}{420}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{199}{210}\right)$$ $$e\left(\frac{383}{420}\right)$$ $$e\left(\frac{317}{420}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{129}{140}\right)$$ $$e\left(\frac{29}{105}\right)$$
$$\chi_{4730}(87,\cdot)$$ 4730.l 4 no $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$i$$ $$1$$
$$\chi_{4730}(89,\cdot)$$ 4730.ck 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$