# Properties

 Modulus $4729$ Structure $$C_{4728}$$ Order $4728$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4729)

pari: g = idealstar(,4729,2)

## Character group

 sage: G.order()  pari: g.no Order = 4728 sage: H.invariants()  pari: g.cyc Structure = $$C_{4728}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4729}(17,\cdot)$

## First 32 of 4728 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{4729}(1,\cdot)$$ 4729.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4729}(2,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{153}{394}\right)$$ $$e\left(\frac{171}{394}\right)$$ $$e\left(\frac{153}{197}\right)$$ $$e\left(\frac{87}{394}\right)$$ $$e\left(\frac{162}{197}\right)$$ $$e\left(\frac{13}{394}\right)$$ $$e\left(\frac{65}{394}\right)$$ $$e\left(\frac{171}{197}\right)$$ $$e\left(\frac{120}{197}\right)$$ $$e\left(\frac{143}{788}\right)$$
$$\chi_{4729}(3,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{171}{394}\right)$$ $$e\left(\frac{307}{394}\right)$$ $$e\left(\frac{171}{197}\right)$$ $$e\left(\frac{329}{394}\right)$$ $$e\left(\frac{42}{197}\right)$$ $$e\left(\frac{339}{394}\right)$$ $$e\left(\frac{119}{394}\right)$$ $$e\left(\frac{110}{197}\right)$$ $$e\left(\frac{53}{197}\right)$$ $$e\left(\frac{183}{788}\right)$$
$$\chi_{4729}(4,\cdot)$$ 4729.j 394 yes $$1$$ $$1$$ $$e\left(\frac{153}{197}\right)$$ $$e\left(\frac{171}{197}\right)$$ $$e\left(\frac{109}{197}\right)$$ $$e\left(\frac{87}{197}\right)$$ $$e\left(\frac{127}{197}\right)$$ $$e\left(\frac{13}{197}\right)$$ $$e\left(\frac{65}{197}\right)$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{43}{197}\right)$$ $$e\left(\frac{143}{394}\right)$$
$$\chi_{4729}(5,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{87}{394}\right)$$ $$e\left(\frac{329}{394}\right)$$ $$e\left(\frac{87}{197}\right)$$ $$e\left(\frac{751}{1182}\right)$$ $$e\left(\frac{11}{197}\right)$$ $$e\left(\frac{787}{1182}\right)$$ $$e\left(\frac{261}{394}\right)$$ $$e\left(\frac{132}{197}\right)$$ $$e\left(\frac{506}{591}\right)$$ $$e\left(\frac{259}{788}\right)$$
$$\chi_{4729}(6,\cdot)$$ 4729.j 394 yes $$1$$ $$1$$ $$e\left(\frac{162}{197}\right)$$ $$e\left(\frac{42}{197}\right)$$ $$e\left(\frac{127}{197}\right)$$ $$e\left(\frac{11}{197}\right)$$ $$e\left(\frac{7}{197}\right)$$ $$e\left(\frac{176}{197}\right)$$ $$e\left(\frac{92}{197}\right)$$ $$e\left(\frac{84}{197}\right)$$ $$e\left(\frac{173}{197}\right)$$ $$e\left(\frac{163}{394}\right)$$
$$\chi_{4729}(7,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{13}{394}\right)$$ $$e\left(\frac{339}{394}\right)$$ $$e\left(\frac{13}{197}\right)$$ $$e\left(\frac{787}{1182}\right)$$ $$e\left(\frac{176}{197}\right)$$ $$e\left(\frac{181}{1182}\right)$$ $$e\left(\frac{39}{394}\right)$$ $$e\left(\frac{142}{197}\right)$$ $$e\left(\frac{413}{591}\right)$$ $$e\left(\frac{401}{788}\right)$$
$$\chi_{4729}(8,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{65}{394}\right)$$ $$e\left(\frac{119}{394}\right)$$ $$e\left(\frac{65}{197}\right)$$ $$e\left(\frac{261}{394}\right)$$ $$e\left(\frac{92}{197}\right)$$ $$e\left(\frac{39}{394}\right)$$ $$e\left(\frac{195}{394}\right)$$ $$e\left(\frac{119}{197}\right)$$ $$e\left(\frac{163}{197}\right)$$ $$e\left(\frac{429}{788}\right)$$
$$\chi_{4729}(9,\cdot)$$ 4729.j 394 yes $$1$$ $$1$$ $$e\left(\frac{171}{197}\right)$$ $$e\left(\frac{110}{197}\right)$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{132}{197}\right)$$ $$e\left(\frac{84}{197}\right)$$ $$e\left(\frac{142}{197}\right)$$ $$e\left(\frac{119}{197}\right)$$ $$e\left(\frac{23}{197}\right)$$ $$e\left(\frac{106}{197}\right)$$ $$e\left(\frac{183}{394}\right)$$
$$\chi_{4729}(10,\cdot)$$ 4729.m 1182 yes $$1$$ $$1$$ $$e\left(\frac{120}{197}\right)$$ $$e\left(\frac{53}{197}\right)$$ $$e\left(\frac{43}{197}\right)$$ $$e\left(\frac{506}{591}\right)$$ $$e\left(\frac{173}{197}\right)$$ $$e\left(\frac{413}{591}\right)$$ $$e\left(\frac{163}{197}\right)$$ $$e\left(\frac{106}{197}\right)$$ $$e\left(\frac{275}{591}\right)$$ $$e\left(\frac{201}{394}\right)$$
$$\chi_{4729}(11,\cdot)$$ 4729.n 1576 yes $$-1$$ $$1$$ $$e\left(\frac{143}{788}\right)$$ $$e\left(\frac{183}{788}\right)$$ $$e\left(\frac{143}{394}\right)$$ $$e\left(\frac{259}{788}\right)$$ $$e\left(\frac{163}{394}\right)$$ $$e\left(\frac{401}{788}\right)$$ $$e\left(\frac{429}{788}\right)$$ $$e\left(\frac{183}{394}\right)$$ $$e\left(\frac{201}{394}\right)$$ $$e\left(\frac{1259}{1576}\right)$$
$$\chi_{4729}(12,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{83}{394}\right)$$ $$e\left(\frac{255}{394}\right)$$ $$e\left(\frac{83}{197}\right)$$ $$e\left(\frac{109}{394}\right)$$ $$e\left(\frac{169}{197}\right)$$ $$e\left(\frac{365}{394}\right)$$ $$e\left(\frac{249}{394}\right)$$ $$e\left(\frac{58}{197}\right)$$ $$e\left(\frac{96}{197}\right)$$ $$e\left(\frac{469}{788}\right)$$
$$\chi_{4729}(13,\cdot)$$ 4729.m 1182 yes $$1$$ $$1$$ $$e\left(\frac{160}{197}\right)$$ $$e\left(\frac{5}{197}\right)$$ $$e\left(\frac{123}{197}\right)$$ $$e\left(\frac{215}{591}\right)$$ $$e\left(\frac{165}{197}\right)$$ $$e\left(\frac{485}{591}\right)$$ $$e\left(\frac{86}{197}\right)$$ $$e\left(\frac{10}{197}\right)$$ $$e\left(\frac{104}{591}\right)$$ $$e\left(\frac{71}{394}\right)$$
$$\chi_{4729}(14,\cdot)$$ 4729.k 591 yes $$1$$ $$1$$ $$e\left(\frac{83}{197}\right)$$ $$e\left(\frac{58}{197}\right)$$ $$e\left(\frac{166}{197}\right)$$ $$e\left(\frac{524}{591}\right)$$ $$e\left(\frac{141}{197}\right)$$ $$e\left(\frac{110}{591}\right)$$ $$e\left(\frac{52}{197}\right)$$ $$e\left(\frac{116}{197}\right)$$ $$e\left(\frac{182}{591}\right)$$ $$e\left(\frac{136}{197}\right)$$
$$\chi_{4729}(15,\cdot)$$ 4729.m 1182 yes $$1$$ $$1$$ $$e\left(\frac{129}{197}\right)$$ $$e\left(\frac{121}{197}\right)$$ $$e\left(\frac{61}{197}\right)$$ $$e\left(\frac{278}{591}\right)$$ $$e\left(\frac{53}{197}\right)$$ $$e\left(\frac{311}{591}\right)$$ $$e\left(\frac{190}{197}\right)$$ $$e\left(\frac{45}{197}\right)$$ $$e\left(\frac{74}{591}\right)$$ $$e\left(\frac{221}{394}\right)$$
$$\chi_{4729}(16,\cdot)$$ 4729.i 197 yes $$1$$ $$1$$ $$e\left(\frac{109}{197}\right)$$ $$e\left(\frac{145}{197}\right)$$ $$e\left(\frac{21}{197}\right)$$ $$e\left(\frac{174}{197}\right)$$ $$e\left(\frac{57}{197}\right)$$ $$e\left(\frac{26}{197}\right)$$ $$e\left(\frac{130}{197}\right)$$ $$e\left(\frac{93}{197}\right)$$ $$e\left(\frac{86}{197}\right)$$ $$e\left(\frac{143}{197}\right)$$
$$\chi_{4729}(17,\cdot)$$ 4729.p 4728 yes $$-1$$ $$1$$ $$e\left(\frac{53}{788}\right)$$ $$e\left(\frac{685}{788}\right)$$ $$e\left(\frac{53}{394}\right)$$ $$e\left(\frac{299}{2364}\right)$$ $$e\left(\frac{369}{394}\right)$$ $$e\left(\frac{1829}{2364}\right)$$ $$e\left(\frac{159}{788}\right)$$ $$e\left(\frac{291}{394}\right)$$ $$e\left(\frac{229}{1182}\right)$$ $$e\left(\frac{1453}{1576}\right)$$
$$\chi_{4729}(18,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{101}{394}\right)$$ $$e\left(\frac{391}{394}\right)$$ $$e\left(\frac{101}{197}\right)$$ $$e\left(\frac{351}{394}\right)$$ $$e\left(\frac{49}{197}\right)$$ $$e\left(\frac{297}{394}\right)$$ $$e\left(\frac{303}{394}\right)$$ $$e\left(\frac{194}{197}\right)$$ $$e\left(\frac{29}{197}\right)$$ $$e\left(\frac{509}{788}\right)$$
$$\chi_{4729}(19,\cdot)$$ 4729.k 591 yes $$1$$ $$1$$ $$e\left(\frac{82}{197}\right)$$ $$e\left(\frac{138}{197}\right)$$ $$e\left(\frac{164}{197}\right)$$ $$e\left(\frac{221}{591}\right)$$ $$e\left(\frac{23}{197}\right)$$ $$e\left(\frac{581}{591}\right)$$ $$e\left(\frac{49}{197}\right)$$ $$e\left(\frac{79}{197}\right)$$ $$e\left(\frac{467}{591}\right)$$ $$e\left(\frac{113}{197}\right)$$
$$\chi_{4729}(20,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{393}{394}\right)$$ $$e\left(\frac{277}{394}\right)$$ $$e\left(\frac{196}{197}\right)$$ $$e\left(\frac{91}{1182}\right)$$ $$e\left(\frac{138}{197}\right)$$ $$e\left(\frac{865}{1182}\right)$$ $$e\left(\frac{391}{394}\right)$$ $$e\left(\frac{80}{197}\right)$$ $$e\left(\frac{44}{591}\right)$$ $$e\left(\frac{545}{788}\right)$$
$$\chi_{4729}(21,\cdot)$$ 4729.k 591 yes $$1$$ $$1$$ $$e\left(\frac{92}{197}\right)$$ $$e\left(\frac{126}{197}\right)$$ $$e\left(\frac{184}{197}\right)$$ $$e\left(\frac{296}{591}\right)$$ $$e\left(\frac{21}{197}\right)$$ $$e\left(\frac{8}{591}\right)$$ $$e\left(\frac{79}{197}\right)$$ $$e\left(\frac{55}{197}\right)$$ $$e\left(\frac{572}{591}\right)$$ $$e\left(\frac{146}{197}\right)$$
$$\chi_{4729}(22,\cdot)$$ 4729.n 1576 yes $$-1$$ $$1$$ $$e\left(\frac{449}{788}\right)$$ $$e\left(\frac{525}{788}\right)$$ $$e\left(\frac{55}{394}\right)$$ $$e\left(\frac{433}{788}\right)$$ $$e\left(\frac{93}{394}\right)$$ $$e\left(\frac{427}{788}\right)$$ $$e\left(\frac{559}{788}\right)$$ $$e\left(\frac{131}{394}\right)$$ $$e\left(\frac{47}{394}\right)$$ $$e\left(\frac{1545}{1576}\right)$$
$$\chi_{4729}(23,\cdot)$$ 4729.n 1576 yes $$-1$$ $$1$$ $$e\left(\frac{29}{788}\right)$$ $$e\left(\frac{241}{788}\right)$$ $$e\left(\frac{29}{394}\right)$$ $$e\left(\frac{565}{788}\right)$$ $$e\left(\frac{135}{394}\right)$$ $$e\left(\frac{175}{788}\right)$$ $$e\left(\frac{87}{788}\right)$$ $$e\left(\frac{241}{394}\right)$$ $$e\left(\frac{297}{394}\right)$$ $$e\left(\frac{349}{1576}\right)$$
$$\chi_{4729}(24,\cdot)$$ 4729.i 197 yes $$1$$ $$1$$ $$e\left(\frac{118}{197}\right)$$ $$e\left(\frac{16}{197}\right)$$ $$e\left(\frac{39}{197}\right)$$ $$e\left(\frac{98}{197}\right)$$ $$e\left(\frac{134}{197}\right)$$ $$e\left(\frac{189}{197}\right)$$ $$e\left(\frac{157}{197}\right)$$ $$e\left(\frac{32}{197}\right)$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{153}{197}\right)$$
$$\chi_{4729}(25,\cdot)$$ 4729.m 1182 yes $$1$$ $$1$$ $$e\left(\frac{87}{197}\right)$$ $$e\left(\frac{132}{197}\right)$$ $$e\left(\frac{174}{197}\right)$$ $$e\left(\frac{160}{591}\right)$$ $$e\left(\frac{22}{197}\right)$$ $$e\left(\frac{196}{591}\right)$$ $$e\left(\frac{64}{197}\right)$$ $$e\left(\frac{67}{197}\right)$$ $$e\left(\frac{421}{591}\right)$$ $$e\left(\frac{259}{394}\right)$$
$$\chi_{4729}(26,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{79}{394}\right)$$ $$e\left(\frac{181}{394}\right)$$ $$e\left(\frac{79}{197}\right)$$ $$e\left(\frac{691}{1182}\right)$$ $$e\left(\frac{130}{197}\right)$$ $$e\left(\frac{1009}{1182}\right)$$ $$e\left(\frac{237}{394}\right)$$ $$e\left(\frac{181}{197}\right)$$ $$e\left(\frac{464}{591}\right)$$ $$e\left(\frac{285}{788}\right)$$
$$\chi_{4729}(27,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{119}{394}\right)$$ $$e\left(\frac{133}{394}\right)$$ $$e\left(\frac{119}{197}\right)$$ $$e\left(\frac{199}{394}\right)$$ $$e\left(\frac{126}{197}\right)$$ $$e\left(\frac{229}{394}\right)$$ $$e\left(\frac{357}{394}\right)$$ $$e\left(\frac{133}{197}\right)$$ $$e\left(\frac{159}{197}\right)$$ $$e\left(\frac{549}{788}\right)$$
$$\chi_{4729}(28,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{319}{394}\right)$$ $$e\left(\frac{287}{394}\right)$$ $$e\left(\frac{122}{197}\right)$$ $$e\left(\frac{127}{1182}\right)$$ $$e\left(\frac{106}{197}\right)$$ $$e\left(\frac{259}{1182}\right)$$ $$e\left(\frac{169}{394}\right)$$ $$e\left(\frac{90}{197}\right)$$ $$e\left(\frac{542}{591}\right)$$ $$e\left(\frac{687}{788}\right)$$
$$\chi_{4729}(29,\cdot)$$ 4729.n 1576 yes $$-1$$ $$1$$ $$e\left(\frac{285}{788}\right)$$ $$e\left(\frac{249}{788}\right)$$ $$e\left(\frac{285}{394}\right)$$ $$e\left(\frac{417}{788}\right)$$ $$e\left(\frac{267}{394}\right)$$ $$e\left(\frac{171}{788}\right)$$ $$e\left(\frac{67}{788}\right)$$ $$e\left(\frac{249}{394}\right)$$ $$e\left(\frac{351}{394}\right)$$ $$e\left(\frac{1093}{1576}\right)$$
$$\chi_{4729}(30,\cdot)$$ 4729.o 2364 yes $$1$$ $$1$$ $$e\left(\frac{17}{394}\right)$$ $$e\left(\frac{19}{394}\right)$$ $$e\left(\frac{17}{197}\right)$$ $$e\left(\frac{817}{1182}\right)$$ $$e\left(\frac{18}{197}\right)$$ $$e\left(\frac{661}{1182}\right)$$ $$e\left(\frac{51}{394}\right)$$ $$e\left(\frac{19}{197}\right)$$ $$e\left(\frac{434}{591}\right)$$ $$e\left(\frac{585}{788}\right)$$
$$\chi_{4729}(31,\cdot)$$ 4729.n 1576 yes $$-1$$ $$1$$ $$e\left(\frac{383}{788}\right)$$ $$e\left(\frac{683}{788}\right)$$ $$e\left(\frac{383}{394}\right)$$ $$e\left(\frac{71}{788}\right)$$ $$e\left(\frac{139}{394}\right)$$ $$e\left(\frac{545}{788}\right)$$ $$e\left(\frac{361}{788}\right)$$ $$e\left(\frac{289}{394}\right)$$ $$e\left(\frac{227}{394}\right)$$ $$e\left(\frac{479}{1576}\right)$$
$$\chi_{4729}(32,\cdot)$$ 4729.l 788 yes $$1$$ $$1$$ $$e\left(\frac{371}{394}\right)$$ $$e\left(\frac{67}{394}\right)$$ $$e\left(\frac{174}{197}\right)$$ $$e\left(\frac{41}{394}\right)$$ $$e\left(\frac{22}{197}\right)$$ $$e\left(\frac{65}{394}\right)$$ $$e\left(\frac{325}{394}\right)$$ $$e\left(\frac{67}{197}\right)$$ $$e\left(\frac{9}{197}\right)$$ $$e\left(\frac{715}{788}\right)$$