# Properties

 Modulus 731 Structure $$C_{336}\times C_{2}$$ Order 672

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(731)

pari: g = idealstar(,731,2)

## Character group

 sage: G.order()  pari: g.no Order = 672 sage: H.invariants()  pari: g.cyc Structure = $$C_{336}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{731}(261,\cdot)$, $\chi_{731}(171,\cdot)$

## First 32 of 672 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 2 3 4 5 6 7 8 9 10 11
$$\chi_{731}(1,\cdot)$$ 731.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{731}(2,\cdot)$$ 731.bf 56 yes $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{29}{56}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{25}{56}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{56}\right)$$ $$e\left(\frac{23}{56}\right)$$
$$\chi_{731}(3,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{29}{56}\right)$$ $$e\left(\frac{29}{336}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{305}{336}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{143}{336}\right)$$ $$e\left(\frac{17}{112}\right)$$
$$\chi_{731}(4,\cdot)$$ 731.y 28 yes $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$i$$ $$i$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{731}(5,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{25}{56}\right)$$ $$e\left(\frac{305}{336}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{149}{336}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{137}{168}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{5}{112}\right)$$
$$\chi_{731}(6,\cdot)$$ 731.bc 48 yes $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$i$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{731}(7,\cdot)$$ 731.bd 48 yes $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$i$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{731}(8,\cdot)$$ 731.bf 56 yes $$-1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{56}\right)$$ $$e\left(\frac{13}{56}\right)$$
$$\chi_{731}(9,\cdot)$$ 731.bl 168 yes $$1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{137}{168}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{17}{56}\right)$$
$$\chi_{731}(10,\cdot)$$ 731.bn 336 yes $$-1$$ $$1$$ $$e\left(\frac{3}{56}\right)$$ $$e\left(\frac{143}{336}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{9}{56}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{317}{336}\right)$$ $$e\left(\frac{51}{112}\right)$$
$$\chi_{731}(11,\cdot)$$ 731.bi 112 yes $$-1$$ $$1$$ $$e\left(\frac{23}{56}\right)$$ $$e\left(\frac{17}{112}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{5}{112}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{17}{56}\right)$$ $$e\left(\frac{51}{112}\right)$$ $$e\left(\frac{55}{112}\right)$$
$$\chi_{731}(12,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{41}{336}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{269}{336}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{56}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{179}{336}\right)$$ $$e\left(\frac{109}{112}\right)$$
$$\chi_{731}(13,\cdot)$$ 731.bh 84 yes $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{731}(14,\cdot)$$ 731.bn 336 yes $$-1$$ $$1$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{13}{336}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{241}{336}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{11}{56}\right)$$ $$e\left(\frac{13}{168}\right)$$ $$e\left(\frac{151}{336}\right)$$ $$e\left(\frac{25}{112}\right)$$
$$\chi_{731}(15,\cdot)$$ 731.bl 168 yes $$1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{167}{168}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{59}{168}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{53}{168}\right)$$ $$e\left(\frac{11}{56}\right)$$
$$\chi_{731}(16,\cdot)$$ 731.p 14 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{731}(18,\cdot)$$ 731.ba 42 no $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{731}(19,\cdot)$$ 731.bk 168 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{55}{168}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{25}{168}\right)$$ $$e\left(\frac{39}{56}\right)$$
$$\chi_{731}(20,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{317}{336}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{113}{336}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{55}{56}\right)$$ $$e\left(\frac{149}{168}\right)$$ $$e\left(\frac{335}{336}\right)$$ $$e\left(\frac{97}{112}\right)$$
$$\chi_{731}(21,\cdot)$$ 731.y 28 yes $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$i$$ $$i$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{731}(22,\cdot)$$ 731.bj 112 yes $$1$$ $$1$$ $$e\left(\frac{1}{56}\right)$$ $$e\left(\frac{75}{112}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{55}{112}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{56}\right)$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{57}{112}\right)$$ $$e\left(\frac{101}{112}\right)$$
$$\chi_{731}(23,\cdot)$$ 731.bn 336 yes $$-1$$ $$1$$ $$e\left(\frac{23}{56}\right)$$ $$e\left(\frac{107}{336}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{71}{336}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{107}{168}\right)$$ $$e\left(\frac{209}{336}\right)$$ $$e\left(\frac{111}{112}\right)$$
$$\chi_{731}(24,\cdot)$$ 731.bn 336 yes $$-1$$ $$1$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{215}{336}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{83}{336}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{1}{56}\right)$$ $$e\left(\frac{47}{168}\right)$$ $$e\left(\frac{197}{336}\right)$$ $$e\left(\frac{43}{112}\right)$$
$$\chi_{731}(25,\cdot)$$ 731.bl 168 yes $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{137}{168}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{149}{168}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{131}{168}\right)$$ $$e\left(\frac{5}{56}\right)$$
$$\chi_{731}(26,\cdot)$$ 731.bk 168 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{89}{168}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{125}{168}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{71}{168}\right)$$ $$e\left(\frac{1}{56}\right)$$
$$\chi_{731}(27,\cdot)$$ 731.bj 112 yes $$1$$ $$1$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{29}{112}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{81}{112}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{29}{56}\right)$$ $$e\left(\frac{31}{112}\right)$$ $$e\left(\frac{51}{112}\right)$$
$$\chi_{731}(28,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{187}{336}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{55}{336}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{1}{56}\right)$$ $$e\left(\frac{19}{168}\right)$$ $$e\left(\frac{169}{336}\right)$$ $$e\left(\frac{71}{112}\right)$$
$$\chi_{731}(29,\cdot)$$ 731.bm 336 yes $$1$$ $$1$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{265}{336}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{157}{336}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{11}{56}\right)$$ $$e\left(\frac{97}{168}\right)$$ $$e\left(\frac{67}{336}\right)$$ $$e\left(\frac{109}{112}\right)$$
$$\chi_{731}(30,\cdot)$$ 731.bg 84 yes $$-1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{731}(31,\cdot)$$ 731.bn 336 yes $$-1$$ $$1$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{125}{336}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{17}{336}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{11}{56}\right)$$ $$e\left(\frac{125}{168}\right)$$ $$e\left(\frac{263}{336}\right)$$ $$e\left(\frac{25}{112}\right)$$
$$\chi_{731}(32,\cdot)$$ 731.bf 56 yes $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{15}{56}\right)$$ $$e\left(\frac{3}{56}\right)$$
$$\chi_{731}(33,\cdot)$$ 731.bb 42 yes $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$