# Properties

 Modulus 4005 Structure $$C_{264}\times C_{4}\times C_{2}$$ Order 2112

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4005)
pari: g = idealstar(,4005,2)

## Character group

 sage: G.order() pari: g.no Order = 2112 sage: H.invariants() pari: g.cyc Structure = $$C_{264}\times C_{4}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{4005}(1427,\cdot)$, $\chi_{4005}(1547,\cdot)$, $\chi_{4005}(179,\cdot)$

## First 32 of 2112 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 4 7 8 11 13 14 16 17 19
$$\chi_{4005}(1,\cdot)$$ 4005.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4005}(2,\cdot)$$ 4005.dt 132 Yes $$1$$ $$1$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{4005}(4,\cdot)$$ 4005.da 66 Yes $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{4005}(7,\cdot)$$ 4005.ed 264 Yes $$1$$ $$1$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{125}{264}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{67}{264}\right)$$ $$e\left(\frac{31}{264}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{63}{88}\right)$$
$$\chi_{4005}(8,\cdot)$$ 4005.ct 44 No $$1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{4005}(11,\cdot)$$ 4005.cz 66 No $$-1$$ $$1$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{4005}(13,\cdot)$$ 4005.ed 264 Yes $$1$$ $$1$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{67}{264}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{245}{264}\right)$$ $$e\left(\frac{137}{264}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{57}{88}\right)$$
$$\chi_{4005}(14,\cdot)$$ 4005.eh 264 Yes $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{31}{264}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{137}{264}\right)$$ $$e\left(\frac{23}{264}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{51}{88}\right)$$
$$\chi_{4005}(16,\cdot)$$ 4005.cm 33 No $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{4005}(17,\cdot)$$ 4005.cw 44 No $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$
$$\chi_{4005}(19,\cdot)$$ 4005.dn 88 No $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{63}{88}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{57}{88}\right)$$ $$e\left(\frac{51}{88}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{81}{88}\right)$$
$$\chi_{4005}(22,\cdot)$$ 4005.dv 132 Yes $$-1$$ $$1$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{83}{132}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{73}{132}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{4005}(23,\cdot)$$ 4005.ef 264 Yes $$-1$$ $$1$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{145}{264}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{215}{264}\right)$$ $$e\left(\frac{131}{264}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{15}{88}\right)$$
$$\chi_{4005}(26,\cdot)$$ 4005.dm 88 No $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{79}{88}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{88}\right)$$ $$e\left(\frac{43}{88}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{45}{88}\right)$$
$$\chi_{4005}(28,\cdot)$$ 4005.dk 88 No $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{67}{88}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{69}{88}\right)$$ $$e\left(\frac{5}{88}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{39}{88}\right)$$
$$\chi_{4005}(29,\cdot)$$ 4005.eh 264 Yes $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{125}{264}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{67}{264}\right)$$ $$e\left(\frac{229}{264}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{41}{88}\right)$$
$$\chi_{4005}(31,\cdot)$$ 4005.eg 264 No $$-1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{229}{264}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{203}{264}\right)$$ $$e\left(\frac{221}{264}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{29}{88}\right)$$
$$\chi_{4005}(32,\cdot)$$ 4005.dt 132 Yes $$1$$ $$1$$ $$e\left(\frac{83}{132}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{4005}(34,\cdot)$$ 4005.bv 12 Yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-i$$
$$\chi_{4005}(37,\cdot)$$ 4005.bf 8 No $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{4005}(38,\cdot)$$ 4005.ee 264 Yes $$-1$$ $$1$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{95}{264}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{241}{264}\right)$$ $$e\left(\frac{145}{264}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{69}{88}\right)$$
$$\chi_{4005}(41,\cdot)$$ 4005.eb 264 No $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{175}{264}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{41}{264}\right)$$ $$e\left(\frac{83}{264}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{31}{88}\right)$$
$$\chi_{4005}(43,\cdot)$$ 4005.ec 264 Yes $$1$$ $$1$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{29}{264}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{43}{264}\right)$$ $$e\left(\frac{211}{264}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{88}\right)$$
$$\chi_{4005}(44,\cdot)$$ 4005.bx 22 No $$-1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{4005}(46,\cdot)$$ 4005.dh 88 No $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{88}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{88}\right)$$ $$e\left(\frac{41}{88}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{88}\right)$$
$$\chi_{4005}(47,\cdot)$$ 4005.dq 132 Yes $$1$$ $$1$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{113}{132}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$
$$\chi_{4005}(49,\cdot)$$ 4005.dp 132 Yes $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{67}{132}\right)$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$
$$\chi_{4005}(52,\cdot)$$ 4005.cj 24 Yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{4005}(53,\cdot)$$ 4005.cq 44 No $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{4005}(56,\cdot)$$ 4005.eb 264 No $$1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{107}{264}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{13}{264}\right)$$ $$e\left(\frac{7}{264}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{27}{88}\right)$$
$$\chi_{4005}(58,\cdot)$$ 4005.ed 264 Yes $$1$$ $$1$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{31}{264}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{137}{264}\right)$$ $$e\left(\frac{221}{264}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{29}{88}\right)$$
$$\chi_{4005}(59,\cdot)$$ 4005.eh 264 Yes $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{109}{264}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{107}{264}\right)$$ $$e\left(\frac{149}{264}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{88}\right)$$