# Properties

 Modulus 24704 Structure $$C_{192}\times C_{32}\times C_{2}$$ Order 12288

# Learn more about

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(24704)

pari: g = idealstar(,24704,2)

## Character group

 sage: G.order()  pari: g.no Order = 12288 sage: H.invariants()  pari: g.cyc Structure = $$C_{192}\times C_{32}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{24704}(23937,\cdot)$, $\chi_{24704}(773,\cdot)$, $\chi_{24704}(24319,\cdot)$

## First 37 of 12288 characters

Each row describes a character. When available, the columns show the order of the character, whether the character is primitive, and several values of the character.

order primitive 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
$$\chi_{24704}(1,\cdot)$$ 1 no 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
$$\chi_{24704}(3,\cdot)$$ 32 yes 1 $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$
$$\chi_{24704}(5,\cdot)$$ 192 yes 1 $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{7}{192}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{7}{192}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{139}{192}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{29}{96}\right)$$
$$\chi_{24704}(7,\cdot)$$ 48 no 1 $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{25}{48}\right)$$ 1 $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{24704}(9,\cdot)$$ 16 no 1 $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{24704}(11,\cdot)$$ 64 yes 1 $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$
$$\chi_{24704}(13,\cdot)$$ 64 yes 1 $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{21}{32}\right)$$
$$\chi_{24704}(15,\cdot)$$ 192 no 1 $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{43}{192}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{65}{192}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$-i$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{137}{192}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{24704}(17,\cdot)$$ 192 no 1 $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{43}{192}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{131}{192}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$i$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{139}{192}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{24704}(19,\cdot)$$ 192 yes 1 $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{5}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{47}{96}\right)$$
$$\chi_{24704}(21,\cdot)$$ 96 yes 1 $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{79}{96}\right)$$
$$\chi_{24704}(23,\cdot)$$ 32 no 1 $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$i$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{24704}(25,\cdot)$$ 96 no 1 $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{24704}(27,\cdot)$$ 32 yes 1 $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{24704}(29,\cdot)$$ 64 yes 1 $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$
$$\chi_{24704}(31,\cdot)$$ 96 no 1 $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{95}{96}\right)$$ 1 $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{24704}(33,\cdot)$$ 64 no 1 $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$i$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{24704}(35,\cdot)$$ 64 yes 1 $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{24704}(37,\cdot)$$ 192 yes 1 $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{65}{192}\right)$$ $$e\left(\frac{131}{192}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{71}{192}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{167}{192}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{53}{192}\right)$$ $$e\left(\frac{13}{96}\right)$$
$$\chi_{24704}(39,\cdot)$$ 64 no 1 $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{47}{64}\right)$$ 1 $$i$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{15}{64}\right)$$ 1 $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$-1$$ $$e\left(\frac{63}{64}\right)$$ $$-1$$
$$\chi_{24704}(41,\cdot)$$ 192 no 1 $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{139}{192}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{71}{192}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{169}{192}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{24704}(43,\cdot)$$ 32 yes 1 $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ 1 $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ 1 $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{24704}(45,\cdot)$$ 192 yes 1 $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{167}{192}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{29}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{167}{192}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{49}{192}\right)$$ $$e\left(\frac{95}{96}\right)$$
$$\chi_{24704}(47,\cdot)$$ 192 no 1 $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{5}{192}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{11}{192}\right)$$ 1 $$e\left(\frac{29}{192}\right)$$ $$e\left(\frac{73}{192}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{95}{192}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{65}{192}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{24704}(49,\cdot)$$ 24 no 1 $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ 1 $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{24704}(51,\cdot)$$ 192 yes 1 $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{95}{192}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{59}{96}\right)$$
$$\chi_{24704}(53,\cdot)$$ 192 yes 1 $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{137}{192}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{167}{192}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{173}{192}\right)$$ $$e\left(\frac{1}{96}\right)$$
$$\chi_{24704}(55,\cdot)$$ 48 no 1 $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{24704}(57,\cdot)$$ 192 no 1 $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{139}{192}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{53}{192}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{49}{192}\right)$$ $$e\left(\frac{65}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{173}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{49}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{24704}(59,\cdot)$$ 96 yes 1 $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{59}{96}\right)$$
$$\chi_{24704}(61,\cdot)$$ 192 yes 1 $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{29}{192}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{149}{192}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{43}{192}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{95}{192}\right)$$ $$e\left(\frac{31}{96}\right)$$
$$\chi_{24704}(63,\cdot)$$ 12 no 1 1 $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ 1 $$i$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ 1 $$e\left(\frac{5}{6}\right)$$ 1 $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ 1 $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{24704}(65,\cdot)$$ 96 no 1 $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$i$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{24704}(67,\cdot)$$ 32 yes 1 $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$-i$$ $$e\left(\frac{11}{32}\right)$$ 1 $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ 1 $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$
$$\chi_{24704}(69,\cdot)$$ 32 yes 1 $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ 1 $$e\left(\frac{25}{32}\right)$$ 1 $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$i$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$
$$\chi_{24704}(71,\cdot)$$ 64 no 1 $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{63}{64}\right)$$ 1 $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ 1 $$e\left(\frac{15}{64}\right)$$ $$-i$$
$$\chi_{24704}(73,\cdot)$$ 192 no 1 $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{7}{192}\right)$$ $$e\left(\frac{181}{192}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{37}{192}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{179}{192}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{5}{6}\right)$$