# Properties

 Modulus $4830$ Structure $$C_{132}\times C_{2}\times C_{2}\times C_{2}$$ Order $1056$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4830)

pari: g = idealstar(,4830,2)

## Character group

 sage: G.order()  pari: g.no Order = 1056 sage: H.invariants()  pari: g.cyc Structure = $$C_{132}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4830}(3221,\cdot)$, $\chi_{4830}(967,\cdot)$, $\chi_{4830}(2761,\cdot)$, $\chi_{4830}(1891,\cdot)$

## 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$
$$\chi_{4830}(1,\cdot)$$ 4830.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4830}(11,\cdot)$$ 4830.de 66 no $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(13,\cdot)$$ 4830.co 44 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$i$$
$$\chi_{4830}(17,\cdot)$$ 4830.do 132 no $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4830}(19,\cdot)$$ 4830.cx 66 no $$1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4830}(29,\cdot)$$ 4830.cj 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$1$$
$$\chi_{4830}(31,\cdot)$$ 4830.dg 66 no $$-1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(37,\cdot)$$ 4830.dn 132 no $$1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4830}(41,\cdot)$$ 4830.cl 22 no $$1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$1$$
$$\chi_{4830}(43,\cdot)$$ 4830.cs 44 no $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$-i$$
$$\chi_{4830}(47,\cdot)$$ 4830.bu 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4830}(53,\cdot)$$ 4830.dq 132 no $$-1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4830}(59,\cdot)$$ 4830.cw 66 no $$1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(61,\cdot)$$ 4830.db 66 no $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(67,\cdot)$$ 4830.dn 132 no $$1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{7}{132}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4830}(71,\cdot)$$ 4830.cf 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$-1$$
$$\chi_{4830}(73,\cdot)$$ 4830.dr 132 no $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{119}{132}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4830}(79,\cdot)$$ 4830.cz 66 no $$-1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(83,\cdot)$$ 4830.cp 44 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$-i$$
$$\chi_{4830}(89,\cdot)$$ 4830.df 66 no $$-1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(97,\cdot)$$ 4830.cu 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$-i$$
$$\chi_{4830}(101,\cdot)$$ 4830.da 66 no $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4830}(103,\cdot)$$ 4830.dl 132 no $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{59}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{1}{132}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4830}(107,\cdot)$$ 4830.dq 132 no $$-1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4830}(109,\cdot)$$ 4830.cz 66 no $$-1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(113,\cdot)$$ 4830.cn 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$i$$
$$\chi_{4830}(121,\cdot)$$ 4830.cm 33 no $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4830}(127,\cdot)$$ 4830.cq 44 no $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$i$$
$$\chi_{4830}(131,\cdot)$$ 4830.da 66 no $$1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4830}(137,\cdot)$$ 4830.bq 12 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4830}(139,\cdot)$$ 4830.o 2 no $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{4830}(143,\cdot)$$ 4830.do 132 no $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{1}{12}\right)$$