# Properties

 Modulus $1216$ Structure $$C_{2}\times C_{2}\times C_{144}$$ Order $576$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1216)

pari: g = idealstar(,1216,2)

## Character group

 sage: G.order()  pari: g.no Order = 576 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{144}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1216}(191,\cdot)$, $\chi_{1216}(837,\cdot)$, $\chi_{1216}(705,\cdot)$

## First 32 of 576 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$21$$ $$23$$
$$\chi_{1216}(1,\cdot)$$ 1216.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1216}(3,\cdot)$$ 1216.ch 144 yes $$1$$ $$1$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{107}{144}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{65}{72}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{61}{144}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{23}{144}\right)$$ $$e\left(\frac{41}{72}\right)$$
$$\chi_{1216}(5,\cdot)$$ 1216.cg 144 yes $$1$$ $$1$$ $$e\left(\frac{107}{144}\right)$$ $$e\left(\frac{41}{144}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{35}{72}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{101}{144}\right)$$ $$e\left(\frac{47}{72}\right)$$
$$\chi_{1216}(7,\cdot)$$ 1216.bo 24 no $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1216}(9,\cdot)$$ 1216.ca 72 no $$1$$ $$1$$ $$e\left(\frac{65}{72}\right)$$ $$e\left(\frac{35}{72}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{23}{72}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{1216}(11,\cdot)$$ 1216.bz 48 yes $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{1216}(13,\cdot)$$ 1216.cf 144 yes $$-1$$ $$1$$ $$e\left(\frac{61}{144}\right)$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{67}{144}\right)$$ $$e\left(\frac{49}{72}\right)$$
$$\chi_{1216}(15,\cdot)$$ 1216.bs 36 no $$1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{1216}(17,\cdot)$$ 1216.bu 36 no $$1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{1216}(21,\cdot)$$ 1216.cf 144 yes $$-1$$ $$1$$ $$e\left(\frac{23}{144}\right)$$ $$e\left(\frac{101}{144}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{23}{72}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{67}{144}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{89}{144}\right)$$ $$e\left(\frac{35}{72}\right)$$
$$\chi_{1216}(23,\cdot)$$ 1216.cc 72 no $$-1$$ $$1$$ $$e\left(\frac{41}{72}\right)$$ $$e\left(\frac{47}{72}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{35}{72}\right)$$ $$e\left(\frac{35}{36}\right)$$
$$\chi_{1216}(25,\cdot)$$ 1216.ca 72 no $$1$$ $$1$$ $$e\left(\frac{35}{72}\right)$$ $$e\left(\frac{41}{72}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{55}{72}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{29}{72}\right)$$ $$e\left(\frac{11}{36}\right)$$
$$\chi_{1216}(27,\cdot)$$ 1216.bw 48 yes $$1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{1216}(29,\cdot)$$ 1216.cf 144 yes $$-1$$ $$1$$ $$e\left(\frac{49}{144}\right)$$ $$e\left(\frac{115}{144}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{5}{144}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{127}{144}\right)$$ $$e\left(\frac{37}{72}\right)$$
$$\chi_{1216}(31,\cdot)$$ 1216.s 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1216}(33,\cdot)$$ 1216.bi 18 no $$-1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1216}(35,\cdot)$$ 1216.ce 144 yes $$-1$$ $$1$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{35}{144}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{65}{72}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{61}{144}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{23}{144}\right)$$ $$e\left(\frac{41}{72}\right)$$
$$\chi_{1216}(37,\cdot)$$ 1216.bg 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1216}(39,\cdot)$$ 1216.x 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$
$$\chi_{1216}(41,\cdot)$$ 1216.cd 72 no $$-1$$ $$1$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{31}{72}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{53}{72}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{72}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{1216}(43,\cdot)$$ 1216.ce 144 yes $$-1$$ $$1$$ $$e\left(\frac{71}{144}\right)$$ $$e\left(\frac{5}{144}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{71}{72}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{91}{144}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{47}{72}\right)$$
$$\chi_{1216}(45,\cdot)$$ 1216.bx 48 yes $$1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{1216}(47,\cdot)$$ 1216.bt 36 no $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{1216}(49,\cdot)$$ 1216.z 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1216}(51,\cdot)$$ 1216.ch 144 yes $$1$$ $$1$$ $$e\left(\frac{133}{144}\right)$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{67}{144}\right)$$ $$e\left(\frac{13}{72}\right)$$
$$\chi_{1216}(53,\cdot)$$ 1216.cf 144 yes $$-1$$ $$1$$ $$e\left(\frac{127}{144}\right)$$ $$e\left(\frac{13}{144}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{55}{72}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{107}{144}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{97}{144}\right)$$ $$e\left(\frac{43}{72}\right)$$
$$\chi_{1216}(55,\cdot)$$ 1216.cc 72 no $$-1$$ $$1$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{19}{72}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{29}{72}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{31}{72}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{1216}(59,\cdot)$$ 1216.ch 144 yes $$1$$ $$1$$ $$e\left(\frac{59}{144}\right)$$ $$e\left(\frac{137}{144}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{59}{72}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{31}{144}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{125}{144}\right)$$ $$e\left(\frac{35}{72}\right)$$
$$\chi_{1216}(61,\cdot)$$ 1216.cg 144 yes $$1$$ $$1$$ $$e\left(\frac{1}{144}\right)$$ $$e\left(\frac{139}{144}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{53}{144}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{79}{144}\right)$$ $$e\left(\frac{61}{72}\right)$$
$$\chi_{1216}(63,\cdot)$$ 1216.bn 18 no $$-1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{1216}(65,\cdot)$$ 1216.r 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1216}(67,\cdot)$$ 1216.ch 144 yes $$1$$ $$1$$ $$e\left(\frac{49}{144}\right)$$ $$e\left(\frac{43}{144}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{77}{144}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{1}{72}\right)$$