# Properties

 Modulus $1157$ Structure $$C_{264}\times C_{4}$$ Order $1056$

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(1157)

pari: g = idealstar(,1157,2)

## Character group

 sage: G.order()  pari: g.no Order = 1056 sage: H.invariants()  pari: g.cyc Structure = $$C_{264}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1157}(982,\cdot)$, $\chi_{1157}(34,\cdot)$

## First 32 of 1056 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{1157}(1,\cdot)$$ 1157.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1157}(2,\cdot)$$ 1157.by 132 yes $$-1$$ $$1$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{67}{132}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{113}{132}\right)$$
$$\chi_{1157}(3,\cdot)$$ 1157.cd 264 yes $$-1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{91}{264}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{227}{264}\right)$$ $$e\left(\frac{155}{264}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{1157}(4,\cdot)$$ 1157.bo 66 yes $$1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$
$$\chi_{1157}(5,\cdot)$$ 1157.bj 44 yes $$-1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$
$$\chi_{1157}(6,\cdot)$$ 1157.cb 264 yes $$1$$ $$1$$ $$e\left(\frac{67}{132}\right)$$ $$e\left(\frac{227}{264}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{97}{264}\right)$$ $$e\left(\frac{61}{264}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{19}{132}\right)$$
$$\chi_{1157}(7,\cdot)$$ 1157.cc 264 yes $$1$$ $$1$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{155}{264}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{264}\right)$$ $$e\left(\frac{169}{264}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{97}{132}\right)$$
$$\chi_{1157}(8,\cdot)$$ 1157.bi 44 yes $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$
$$\chi_{1157}(9,\cdot)$$ 1157.bz 132 yes $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{1157}(10,\cdot)$$ 1157.bu 132 yes $$1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{1157}(11,\cdot)$$ 1157.bv 132 yes $$-1$$ $$1$$ $$e\left(\frac{113}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{35}{132}\right)$$
$$\chi_{1157}(12,\cdot)$$ 1157.o 8 yes $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$i$$ $$1$$
$$\chi_{1157}(14,\cdot)$$ 1157.bq 88 no $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{88}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{65}{88}\right)$$ $$e\left(\frac{25}{88}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{1157}(15,\cdot)$$ 1157.cc 264 yes $$1$$ $$1$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{37}{264}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{264}\right)$$ $$e\left(\frac{71}{264}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{37}{132}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{47}{132}\right)$$
$$\chi_{1157}(16,\cdot)$$ 1157.bg 33 yes $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{1157}(17,\cdot)$$ 1157.bu 132 yes $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$
$$\chi_{1157}(18,\cdot)$$ 1157.bk 44 yes $$-1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$
$$\chi_{1157}(19,\cdot)$$ 1157.cc 264 yes $$1$$ $$1$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{17}{264}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{223}{264}\right)$$ $$e\left(\frac{211}{264}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{43}{132}\right)$$
$$\chi_{1157}(20,\cdot)$$ 1157.bw 132 yes $$-1$$ $$1$$ $$e\left(\frac{61}{132}\right)$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{103}{132}\right)$$
$$\chi_{1157}(21,\cdot)$$ 1157.bj 44 yes $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$
$$\chi_{1157}(22,\cdot)$$ 1157.bp 66 yes $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{1157}(23,\cdot)$$ 1157.ca 264 yes $$-1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{259}{264}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{47}{264}\right)$$ $$e\left(\frac{167}{264}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{1157}(24,\cdot)$$ 1157.cc 264 yes $$1$$ $$1$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{235}{264}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{101}{264}\right)$$ $$e\left(\frac{137}{264}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{113}{132}\right)$$
$$\chi_{1157}(25,\cdot)$$ 1157.bb 22 yes $$1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1157}(27,\cdot)$$ 1157.bq 88 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{88}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{51}{88}\right)$$ $$e\left(\frac{67}{88}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1157}(28,\cdot)$$ 1157.cb 264 yes $$1$$ $$1$$ $$e\left(\frac{83}{132}\right)$$ $$e\left(\frac{163}{264}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{65}{264}\right)$$ $$e\left(\frac{245}{264}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{59}{132}\right)$$
$$\chi_{1157}(29,\cdot)$$ 1157.cd 264 yes $$-1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{264}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{17}{264}\right)$$ $$e\left(\frac{257}{264}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{132}\right)$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{43}{66}\right)$$
$$\chi_{1157}(30,\cdot)$$ 1157.ca 264 yes $$-1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{173}{264}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{169}{264}\right)$$ $$e\left(\frac{241}{264}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{1157}(31,\cdot)$$ 1157.bs 88 yes $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{31}{88}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{65}{88}\right)$$ $$e\left(\frac{69}{88}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$
$$\chi_{1157}(32,\cdot)$$ 1157.by 132 yes $$-1$$ $$1$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{71}{132}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{37}{132}\right)$$
$$\chi_{1157}(33,\cdot)$$ 1157.cc 264 yes $$1$$ $$1$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{167}{264}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{264}\right)$$ $$e\left(\frac{85}{264}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{73}{132}\right)$$
$$\chi_{1157}(34,\cdot)$$ 1157.h 4 yes $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$-i$$