# Properties

 Modulus $4889$ Structure $$C_{4888}$$ Order $4888$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(4889)

pari: g = idealstar(,4889,2)

## Character group

 sage: G.order()  pari: g.no Order = 4888 sage: H.invariants()  pari: g.cyc Structure = $$C_{4888}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4889}(3,\cdot)$

## First 32 of 4888 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{4889}(1,\cdot)$$ 4889.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4889}(2,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{647}{1222}\right)$$ $$e\left(\frac{617}{2444}\right)$$ $$e\left(\frac{36}{611}\right)$$ $$e\left(\frac{419}{611}\right)$$ $$e\left(\frac{147}{188}\right)$$ $$e\left(\frac{1057}{2444}\right)$$ $$e\left(\frac{719}{1222}\right)$$ $$e\left(\frac{617}{1222}\right)$$ $$e\left(\frac{263}{1222}\right)$$ $$e\left(\frac{361}{1222}\right)$$
$$\chi_{4889}(3,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{617}{2444}\right)$$ $$e\left(\frac{1}{4888}\right)$$ $$e\left(\frac{617}{1222}\right)$$ $$e\left(\frac{579}{1222}\right)$$ $$e\left(\frac{95}{376}\right)$$ $$e\left(\frac{889}{4888}\right)$$ $$e\left(\frac{1851}{2444}\right)$$ $$e\left(\frac{1}{2444}\right)$$ $$e\left(\frac{1775}{2444}\right)$$ $$e\left(\frac{1995}{2444}\right)$$
$$\chi_{4889}(4,\cdot)$$ 4889.n 1222 yes $$1$$ $$1$$ $$e\left(\frac{36}{611}\right)$$ $$e\left(\frac{617}{1222}\right)$$ $$e\left(\frac{72}{611}\right)$$ $$e\left(\frac{227}{611}\right)$$ $$e\left(\frac{53}{94}\right)$$ $$e\left(\frac{1057}{1222}\right)$$ $$e\left(\frac{108}{611}\right)$$ $$e\left(\frac{6}{611}\right)$$ $$e\left(\frac{263}{611}\right)$$ $$e\left(\frac{361}{611}\right)$$
$$\chi_{4889}(5,\cdot)$$ 4889.n 1222 yes $$1$$ $$1$$ $$e\left(\frac{419}{611}\right)$$ $$e\left(\frac{579}{1222}\right)$$ $$e\left(\frac{227}{611}\right)$$ $$e\left(\frac{215}{611}\right)$$ $$e\left(\frac{15}{94}\right)$$ $$e\left(\frac{269}{1222}\right)$$ $$e\left(\frac{35}{611}\right)$$ $$e\left(\frac{579}{611}\right)$$ $$e\left(\frac{23}{611}\right)$$ $$e\left(\frac{315}{611}\right)$$
$$\chi_{4889}(6,\cdot)$$ 4889.l 376 yes $$-1$$ $$1$$ $$e\left(\frac{147}{188}\right)$$ $$e\left(\frac{95}{376}\right)$$ $$e\left(\frac{53}{94}\right)$$ $$e\left(\frac{15}{94}\right)$$ $$e\left(\frac{13}{376}\right)$$ $$e\left(\frac{231}{376}\right)$$ $$e\left(\frac{65}{188}\right)$$ $$e\left(\frac{95}{188}\right)$$ $$e\left(\frac{177}{188}\right)$$ $$e\left(\frac{21}{188}\right)$$
$$\chi_{4889}(7,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{1057}{2444}\right)$$ $$e\left(\frac{889}{4888}\right)$$ $$e\left(\frac{1057}{1222}\right)$$ $$e\left(\frac{269}{1222}\right)$$ $$e\left(\frac{231}{376}\right)$$ $$e\left(\frac{3353}{4888}\right)$$ $$e\left(\frac{727}{2444}\right)$$ $$e\left(\frac{889}{2444}\right)$$ $$e\left(\frac{1595}{2444}\right)$$ $$e\left(\frac{1655}{2444}\right)$$
$$\chi_{4889}(8,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{719}{1222}\right)$$ $$e\left(\frac{1851}{2444}\right)$$ $$e\left(\frac{108}{611}\right)$$ $$e\left(\frac{35}{611}\right)$$ $$e\left(\frac{65}{188}\right)$$ $$e\left(\frac{727}{2444}\right)$$ $$e\left(\frac{935}{1222}\right)$$ $$e\left(\frac{629}{1222}\right)$$ $$e\left(\frac{789}{1222}\right)$$ $$e\left(\frac{1083}{1222}\right)$$
$$\chi_{4889}(9,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{617}{1222}\right)$$ $$e\left(\frac{1}{2444}\right)$$ $$e\left(\frac{6}{611}\right)$$ $$e\left(\frac{579}{611}\right)$$ $$e\left(\frac{95}{188}\right)$$ $$e\left(\frac{889}{2444}\right)$$ $$e\left(\frac{629}{1222}\right)$$ $$e\left(\frac{1}{1222}\right)$$ $$e\left(\frac{553}{1222}\right)$$ $$e\left(\frac{773}{1222}\right)$$
$$\chi_{4889}(10,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{263}{1222}\right)$$ $$e\left(\frac{1775}{2444}\right)$$ $$e\left(\frac{263}{611}\right)$$ $$e\left(\frac{23}{611}\right)$$ $$e\left(\frac{177}{188}\right)$$ $$e\left(\frac{1595}{2444}\right)$$ $$e\left(\frac{789}{1222}\right)$$ $$e\left(\frac{553}{1222}\right)$$ $$e\left(\frac{309}{1222}\right)$$ $$e\left(\frac{991}{1222}\right)$$
$$\chi_{4889}(11,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{361}{1222}\right)$$ $$e\left(\frac{1995}{2444}\right)$$ $$e\left(\frac{361}{611}\right)$$ $$e\left(\frac{315}{611}\right)$$ $$e\left(\frac{21}{188}\right)$$ $$e\left(\frac{1655}{2444}\right)$$ $$e\left(\frac{1083}{1222}\right)$$ $$e\left(\frac{773}{1222}\right)$$ $$e\left(\frac{991}{1222}\right)$$ $$e\left(\frac{1193}{1222}\right)$$
$$\chi_{4889}(12,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{761}{2444}\right)$$ $$e\left(\frac{2469}{4888}\right)$$ $$e\left(\frac{761}{1222}\right)$$ $$e\left(\frac{1033}{1222}\right)$$ $$e\left(\frac{307}{376}\right)$$ $$e\left(\frac{229}{4888}\right)$$ $$e\left(\frac{2283}{2444}\right)$$ $$e\left(\frac{25}{2444}\right)$$ $$e\left(\frac{383}{2444}\right)$$ $$e\left(\frac{995}{2444}\right)$$
$$\chi_{4889}(13,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{797}{1222}\right)$$ $$e\left(\frac{1253}{2444}\right)$$ $$e\left(\frac{186}{611}\right)$$ $$e\left(\frac{230}{611}\right)$$ $$e\left(\frac{31}{188}\right)$$ $$e\left(\frac{1897}{2444}\right)$$ $$e\left(\frac{1169}{1222}\right)$$ $$e\left(\frac{31}{1222}\right)$$ $$e\left(\frac{35}{1222}\right)$$ $$e\left(\frac{745}{1222}\right)$$
$$\chi_{4889}(14,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{2351}{2444}\right)$$ $$e\left(\frac{2123}{4888}\right)$$ $$e\left(\frac{1129}{1222}\right)$$ $$e\left(\frac{1107}{1222}\right)$$ $$e\left(\frac{149}{376}\right)$$ $$e\left(\frac{579}{4888}\right)$$ $$e\left(\frac{2165}{2444}\right)$$ $$e\left(\frac{2123}{2444}\right)$$ $$e\left(\frac{2121}{2444}\right)$$ $$e\left(\frac{2377}{2444}\right)$$
$$\chi_{4889}(15,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{2293}{2444}\right)$$ $$e\left(\frac{2317}{4888}\right)$$ $$e\left(\frac{1071}{1222}\right)$$ $$e\left(\frac{1009}{1222}\right)$$ $$e\left(\frac{155}{376}\right)$$ $$e\left(\frac{1965}{4888}\right)$$ $$e\left(\frac{1991}{2444}\right)$$ $$e\left(\frac{2317}{2444}\right)$$ $$e\left(\frac{1867}{2444}\right)$$ $$e\left(\frac{811}{2444}\right)$$
$$\chi_{4889}(16,\cdot)$$ 4889.m 611 yes $$1$$ $$1$$ $$e\left(\frac{72}{611}\right)$$ $$e\left(\frac{6}{611}\right)$$ $$e\left(\frac{144}{611}\right)$$ $$e\left(\frac{454}{611}\right)$$ $$e\left(\frac{6}{47}\right)$$ $$e\left(\frac{446}{611}\right)$$ $$e\left(\frac{216}{611}\right)$$ $$e\left(\frac{12}{611}\right)$$ $$e\left(\frac{526}{611}\right)$$ $$e\left(\frac{111}{611}\right)$$
$$\chi_{4889}(17,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{685}{2444}\right)$$ $$e\left(\frac{4493}{4888}\right)$$ $$e\left(\frac{685}{1222}\right)$$ $$e\left(\frac{1031}{1222}\right)$$ $$e\left(\frac{75}{376}\right)$$ $$e\left(\frac{781}{4888}\right)$$ $$e\left(\frac{2055}{2444}\right)$$ $$e\left(\frac{2049}{2444}\right)$$ $$e\left(\frac{303}{2444}\right)$$ $$e\left(\frac{1387}{2444}\right)$$
$$\chi_{4889}(18,\cdot)$$ 4889.n 1222 yes $$1$$ $$1$$ $$e\left(\frac{21}{611}\right)$$ $$e\left(\frac{309}{1222}\right)$$ $$e\left(\frac{42}{611}\right)$$ $$e\left(\frac{387}{611}\right)$$ $$e\left(\frac{27}{94}\right)$$ $$e\left(\frac{973}{1222}\right)$$ $$e\left(\frac{63}{611}\right)$$ $$e\left(\frac{309}{611}\right)$$ $$e\left(\frac{408}{611}\right)$$ $$e\left(\frac{567}{611}\right)$$
$$\chi_{4889}(19,\cdot)$$ 4889.n 1222 yes $$1$$ $$1$$ $$e\left(\frac{83}{611}\right)$$ $$e\left(\frac{523}{1222}\right)$$ $$e\left(\frac{166}{611}\right)$$ $$e\left(\frac{133}{611}\right)$$ $$e\left(\frac{53}{94}\right)$$ $$e\left(\frac{587}{1222}\right)$$ $$e\left(\frac{249}{611}\right)$$ $$e\left(\frac{523}{611}\right)$$ $$e\left(\frac{216}{611}\right)$$ $$e\left(\frac{408}{611}\right)$$
$$\chi_{4889}(20,\cdot)$$ 4889.g 47 yes $$1$$ $$1$$ $$e\left(\frac{35}{47}\right)$$ $$e\left(\frac{46}{47}\right)$$ $$e\left(\frac{23}{47}\right)$$ $$e\left(\frac{34}{47}\right)$$ $$e\left(\frac{34}{47}\right)$$ $$e\left(\frac{4}{47}\right)$$ $$e\left(\frac{11}{47}\right)$$ $$e\left(\frac{45}{47}\right)$$ $$e\left(\frac{22}{47}\right)$$ $$e\left(\frac{5}{47}\right)$$
$$\chi_{4889}(21,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{837}{1222}\right)$$ $$e\left(\frac{445}{2444}\right)$$ $$e\left(\frac{226}{611}\right)$$ $$e\left(\frac{424}{611}\right)$$ $$e\left(\frac{163}{188}\right)$$ $$e\left(\frac{2121}{2444}\right)$$ $$e\left(\frac{67}{1222}\right)$$ $$e\left(\frac{445}{1222}\right)$$ $$e\left(\frac{463}{1222}\right)$$ $$e\left(\frac{603}{1222}\right)$$
$$\chi_{4889}(22,\cdot)$$ 4889.m 611 yes $$1$$ $$1$$ $$e\left(\frac{504}{611}\right)$$ $$e\left(\frac{42}{611}\right)$$ $$e\left(\frac{397}{611}\right)$$ $$e\left(\frac{123}{611}\right)$$ $$e\left(\frac{42}{47}\right)$$ $$e\left(\frac{67}{611}\right)$$ $$e\left(\frac{290}{611}\right)$$ $$e\left(\frac{84}{611}\right)$$ $$e\left(\frac{16}{611}\right)$$ $$e\left(\frac{166}{611}\right)$$
$$\chi_{4889}(23,\cdot)$$ 4889.m 611 yes $$1$$ $$1$$ $$e\left(\frac{367}{611}\right)$$ $$e\left(\frac{387}{611}\right)$$ $$e\left(\frac{123}{611}\right)$$ $$e\left(\frac{566}{611}\right)$$ $$e\left(\frac{11}{47}\right)$$ $$e\left(\frac{50}{611}\right)$$ $$e\left(\frac{490}{611}\right)$$ $$e\left(\frac{163}{611}\right)$$ $$e\left(\frac{322}{611}\right)$$ $$e\left(\frac{133}{611}\right)$$
$$\chi_{4889}(24,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{2055}{2444}\right)$$ $$e\left(\frac{3703}{4888}\right)$$ $$e\left(\frac{833}{1222}\right)$$ $$e\left(\frac{649}{1222}\right)$$ $$e\left(\frac{225}{376}\right)$$ $$e\left(\frac{2343}{4888}\right)$$ $$e\left(\frac{1277}{2444}\right)$$ $$e\left(\frac{1259}{2444}\right)$$ $$e\left(\frac{909}{2444}\right)$$ $$e\left(\frac{1717}{2444}\right)$$
$$\chi_{4889}(25,\cdot)$$ 4889.m 611 yes $$1$$ $$1$$ $$e\left(\frac{227}{611}\right)$$ $$e\left(\frac{579}{611}\right)$$ $$e\left(\frac{454}{611}\right)$$ $$e\left(\frac{430}{611}\right)$$ $$e\left(\frac{15}{47}\right)$$ $$e\left(\frac{269}{611}\right)$$ $$e\left(\frac{70}{611}\right)$$ $$e\left(\frac{547}{611}\right)$$ $$e\left(\frac{46}{611}\right)$$ $$e\left(\frac{19}{611}\right)$$
$$\chi_{4889}(26,\cdot)$$ 4889.n 1222 yes $$1$$ $$1$$ $$e\left(\frac{111}{611}\right)$$ $$e\left(\frac{935}{1222}\right)$$ $$e\left(\frac{222}{611}\right)$$ $$e\left(\frac{38}{611}\right)$$ $$e\left(\frac{89}{94}\right)$$ $$e\left(\frac{255}{1222}\right)$$ $$e\left(\frac{333}{611}\right)$$ $$e\left(\frac{324}{611}\right)$$ $$e\left(\frac{149}{611}\right)$$ $$e\left(\frac{553}{611}\right)$$
$$\chi_{4889}(27,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{1851}{2444}\right)$$ $$e\left(\frac{3}{4888}\right)$$ $$e\left(\frac{629}{1222}\right)$$ $$e\left(\frac{515}{1222}\right)$$ $$e\left(\frac{285}{376}\right)$$ $$e\left(\frac{2667}{4888}\right)$$ $$e\left(\frac{665}{2444}\right)$$ $$e\left(\frac{3}{2444}\right)$$ $$e\left(\frac{437}{2444}\right)$$ $$e\left(\frac{1097}{2444}\right)$$
$$\chi_{4889}(28,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{1201}{2444}\right)$$ $$e\left(\frac{3357}{4888}\right)$$ $$e\left(\frac{1201}{1222}\right)$$ $$e\left(\frac{723}{1222}\right)$$ $$e\left(\frac{67}{376}\right)$$ $$e\left(\frac{2693}{4888}\right)$$ $$e\left(\frac{1159}{2444}\right)$$ $$e\left(\frac{913}{2444}\right)$$ $$e\left(\frac{203}{2444}\right)$$ $$e\left(\frac{655}{2444}\right)$$
$$\chi_{4889}(29,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{17}{2444}\right)$$ $$e\left(\frac{2345}{4888}\right)$$ $$e\left(\frac{17}{1222}\right)$$ $$e\left(\frac{113}{1222}\right)$$ $$e\left(\frac{183}{376}\right)$$ $$e\left(\frac{2417}{4888}\right)$$ $$e\left(\frac{51}{2444}\right)$$ $$e\left(\frac{2345}{2444}\right)$$ $$e\left(\frac{243}{2444}\right)$$ $$e\left(\frac{459}{2444}\right)$$
$$\chi_{4889}(30,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{1143}{2444}\right)$$ $$e\left(\frac{3551}{4888}\right)$$ $$e\left(\frac{1143}{1222}\right)$$ $$e\left(\frac{625}{1222}\right)$$ $$e\left(\frac{73}{376}\right)$$ $$e\left(\frac{4079}{4888}\right)$$ $$e\left(\frac{985}{2444}\right)$$ $$e\left(\frac{1107}{2444}\right)$$ $$e\left(\frac{2393}{2444}\right)$$ $$e\left(\frac{1533}{2444}\right)$$
$$\chi_{4889}(31,\cdot)$$ 4889.p 4888 yes $$-1$$ $$1$$ $$e\left(\frac{71}{2444}\right)$$ $$e\left(\frac{1743}{4888}\right)$$ $$e\left(\frac{71}{1222}\right)$$ $$e\left(\frac{1047}{1222}\right)$$ $$e\left(\frac{145}{376}\right)$$ $$e\left(\frac{31}{4888}\right)$$ $$e\left(\frac{213}{2444}\right)$$ $$e\left(\frac{1743}{2444}\right)$$ $$e\left(\frac{2165}{2444}\right)$$ $$e\left(\frac{1917}{2444}\right)$$
$$\chi_{4889}(32,\cdot)$$ 4889.o 2444 yes $$1$$ $$1$$ $$e\left(\frac{791}{1222}\right)$$ $$e\left(\frac{641}{2444}\right)$$ $$e\left(\frac{180}{611}\right)$$ $$e\left(\frac{262}{611}\right)$$ $$e\left(\frac{171}{188}\right)$$ $$e\left(\frac{397}{2444}\right)$$ $$e\left(\frac{1151}{1222}\right)$$ $$e\left(\frac{641}{1222}\right)$$ $$e\left(\frac{93}{1222}\right)$$ $$e\left(\frac{583}{1222}\right)$$