# Properties

 Modulus $2304$ Structure $$C_{2}\times C_{2}\times C_{192}$$ Order $768$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2304)

pari: g = idealstar(,2304,2)

## Character group

 sage: G.order()  pari: g.no Order = 768 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{192}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2304}(1279,\cdot)$, $\chi_{2304}(2053,\cdot)$, $\chi_{2304}(1793,\cdot)$

## First 32 of 768 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{2304}(1,\cdot)$$ 2304.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2304}(5,\cdot)$$ 2304.cb 192 yes $$-1$$ $$1$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{77}{192}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{145}{192}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{2304}(7,\cdot)$$ 2304.by 96 no $$-1$$ $$1$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2304}(11,\cdot)$$ 2304.cd 192 yes $$1$$ $$1$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{145}{192}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{2304}(13,\cdot)$$ 2304.ca 192 yes $$1$$ $$1$$ $$e\left(\frac{77}{192}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{145}{192}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{2304}(17,\cdot)$$ 2304.bc 16 no $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$
$$\chi_{2304}(19,\cdot)$$ 2304.bv 64 no $$-1$$ $$1$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{2304}(23,\cdot)$$ 2304.bw 96 no $$1$$ $$1$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2304}(25,\cdot)$$ 2304.bz 96 no $$1$$ $$1$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2304}(29,\cdot)$$ 2304.cb 192 yes $$-1$$ $$1$$ $$e\left(\frac{145}{192}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{2304}(31,\cdot)$$ 2304.bh 24 no $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2304}(35,\cdot)$$ 2304.bu 64 no $$1$$ $$1$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{2304}(37,\cdot)$$ 2304.bt 64 no $$1$$ $$1$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{2304}(41,\cdot)$$ 2304.bx 96 no $$-1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2304}(43,\cdot)$$ 2304.cc 192 yes $$-1$$ $$1$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{173}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{2304}(47,\cdot)$$ 2304.bp 48 no $$1$$ $$1$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$-i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2304}(49,\cdot)$$ 2304.bq 48 no $$1$$ $$1$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2304}(53,\cdot)$$ 2304.bs 64 no $$-1$$ $$1$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{2304}(55,\cdot)$$ 2304.bk 32 no $$-1$$ $$1$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$i$$
$$\chi_{2304}(59,\cdot)$$ 2304.cd 192 yes $$1$$ $$1$$ $$e\left(\frac{83}{192}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{29}{192}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{2304}(61,\cdot)$$ 2304.ca 192 yes $$1$$ $$1$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{173}{192}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{2304}(65,\cdot)$$ 2304.ba 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2304}(67,\cdot)$$ 2304.cc 192 yes $$-1$$ $$1$$ $$e\left(\frac{89}{192}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{23}{192}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{2304}(71,\cdot)$$ 2304.bm 32 no $$1$$ $$1$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$-i$$
$$\chi_{2304}(73,\cdot)$$ 2304.bl 32 no $$1$$ $$1$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$-i$$
$$\chi_{2304}(77,\cdot)$$ 2304.cb 192 yes $$-1$$ $$1$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{83}{192}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{2304}(79,\cdot)$$ 2304.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2304}(83,\cdot)$$ 2304.cd 192 yes $$1$$ $$1$$ $$e\left(\frac{85}{192}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{89}{192}\right)$$ $$e\left(\frac{187}{192}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{23}{192}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{2304}(85,\cdot)$$ 2304.ca 192 yes $$1$$ $$1$$ $$e\left(\frac{23}{192}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{163}{192}\right)$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{2304}(89,\cdot)$$ 2304.bn 32 no $$-1$$ $$1$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$i$$
$$\chi_{2304}(91,\cdot)$$ 2304.bv 64 no $$-1$$ $$1$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{2304}(95,\cdot)$$ 2304.bj 24 no $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$