Properties

 Modulus $5077$ Structure $$C_{5076}$$ Order $5076$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5077)

pari: g = idealstar(,5077,2)

Character group

 sage: G.order()  pari: g.no Order = 5076 sage: H.invariants()  pari: g.cyc Structure = $$C_{5076}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5077}(2,\cdot)$

First 32 of 5076 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{5077}(1,\cdot)$$ 5077.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5077}(2,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{1}{5076}\right)$$ $$e\left(\frac{727}{846}\right)$$ $$e\left(\frac{1}{2538}\right)$$ $$e\left(\frac{11}{188}\right)$$ $$e\left(\frac{4363}{5076}\right)$$ $$e\left(\frac{343}{1269}\right)$$ $$e\left(\frac{1}{1692}\right)$$ $$e\left(\frac{304}{423}\right)$$ $$e\left(\frac{149}{2538}\right)$$ $$e\left(\frac{2357}{5076}\right)$$
$$\chi_{5077}(3,\cdot)$$ 5077.t 846 yes $$1$$ $$1$$ $$e\left(\frac{727}{846}\right)$$ $$e\left(\frac{61}{141}\right)$$ $$e\left(\frac{304}{423}\right)$$ $$e\left(\frac{21}{94}\right)$$ $$e\left(\frac{247}{846}\right)$$ $$e\left(\frac{5}{423}\right)$$ $$e\left(\frac{163}{282}\right)$$ $$e\left(\frac{122}{141}\right)$$ $$e\left(\frac{35}{423}\right)$$ $$e\left(\frac{389}{846}\right)$$
$$\chi_{5077}(4,\cdot)$$ 5077.w 2538 yes $$1$$ $$1$$ $$e\left(\frac{1}{2538}\right)$$ $$e\left(\frac{304}{423}\right)$$ $$e\left(\frac{1}{1269}\right)$$ $$e\left(\frac{11}{94}\right)$$ $$e\left(\frac{1825}{2538}\right)$$ $$e\left(\frac{686}{1269}\right)$$ $$e\left(\frac{1}{846}\right)$$ $$e\left(\frac{185}{423}\right)$$ $$e\left(\frac{149}{1269}\right)$$ $$e\left(\frac{2357}{2538}\right)$$
$$\chi_{5077}(5,\cdot)$$ 5077.p 188 yes $$-1$$ $$1$$ $$e\left(\frac{11}{188}\right)$$ $$e\left(\frac{21}{94}\right)$$ $$e\left(\frac{11}{94}\right)$$ $$e\left(\frac{71}{188}\right)$$ $$e\left(\frac{53}{188}\right)$$ $$e\left(\frac{13}{47}\right)$$ $$e\left(\frac{33}{188}\right)$$ $$e\left(\frac{21}{47}\right)$$ $$e\left(\frac{41}{94}\right)$$ $$e\left(\frac{171}{188}\right)$$
$$\chi_{5077}(6,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{4363}{5076}\right)$$ $$e\left(\frac{247}{846}\right)$$ $$e\left(\frac{1825}{2538}\right)$$ $$e\left(\frac{53}{188}\right)$$ $$e\left(\frac{769}{5076}\right)$$ $$e\left(\frac{358}{1269}\right)$$ $$e\left(\frac{979}{1692}\right)$$ $$e\left(\frac{247}{423}\right)$$ $$e\left(\frac{359}{2538}\right)$$ $$e\left(\frac{4691}{5076}\right)$$
$$\chi_{5077}(7,\cdot)$$ 5077.u 1269 yes $$1$$ $$1$$ $$e\left(\frac{343}{1269}\right)$$ $$e\left(\frac{5}{423}\right)$$ $$e\left(\frac{686}{1269}\right)$$ $$e\left(\frac{13}{47}\right)$$ $$e\left(\frac{358}{1269}\right)$$ $$e\left(\frac{1066}{1269}\right)$$ $$e\left(\frac{343}{423}\right)$$ $$e\left(\frac{10}{423}\right)$$ $$e\left(\frac{694}{1269}\right)$$ $$e\left(\frac{98}{1269}\right)$$
$$\chi_{5077}(8,\cdot)$$ 5077.v 1692 yes $$-1$$ $$1$$ $$e\left(\frac{1}{1692}\right)$$ $$e\left(\frac{163}{282}\right)$$ $$e\left(\frac{1}{846}\right)$$ $$e\left(\frac{33}{188}\right)$$ $$e\left(\frac{979}{1692}\right)$$ $$e\left(\frac{343}{423}\right)$$ $$e\left(\frac{1}{564}\right)$$ $$e\left(\frac{22}{141}\right)$$ $$e\left(\frac{149}{846}\right)$$ $$e\left(\frac{665}{1692}\right)$$
$$\chi_{5077}(9,\cdot)$$ 5077.r 423 yes $$1$$ $$1$$ $$e\left(\frac{304}{423}\right)$$ $$e\left(\frac{122}{141}\right)$$ $$e\left(\frac{185}{423}\right)$$ $$e\left(\frac{21}{47}\right)$$ $$e\left(\frac{247}{423}\right)$$ $$e\left(\frac{10}{423}\right)$$ $$e\left(\frac{22}{141}\right)$$ $$e\left(\frac{103}{141}\right)$$ $$e\left(\frac{70}{423}\right)$$ $$e\left(\frac{389}{423}\right)$$
$$\chi_{5077}(10,\cdot)$$ 5077.w 2538 yes $$1$$ $$1$$ $$e\left(\frac{149}{2538}\right)$$ $$e\left(\frac{35}{423}\right)$$ $$e\left(\frac{149}{1269}\right)$$ $$e\left(\frac{41}{94}\right)$$ $$e\left(\frac{359}{2538}\right)$$ $$e\left(\frac{694}{1269}\right)$$ $$e\left(\frac{149}{846}\right)$$ $$e\left(\frac{70}{423}\right)$$ $$e\left(\frac{628}{1269}\right)$$ $$e\left(\frac{949}{2538}\right)$$
$$\chi_{5077}(11,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{2357}{5076}\right)$$ $$e\left(\frac{389}{846}\right)$$ $$e\left(\frac{2357}{2538}\right)$$ $$e\left(\frac{171}{188}\right)$$ $$e\left(\frac{4691}{5076}\right)$$ $$e\left(\frac{98}{1269}\right)$$ $$e\left(\frac{665}{1692}\right)$$ $$e\left(\frac{389}{423}\right)$$ $$e\left(\frac{949}{2538}\right)$$ $$e\left(\frac{2305}{5076}\right)$$
$$\chi_{5077}(12,\cdot)$$ 5077.u 1269 yes $$1$$ $$1$$ $$e\left(\frac{1091}{1269}\right)$$ $$e\left(\frac{64}{423}\right)$$ $$e\left(\frac{913}{1269}\right)$$ $$e\left(\frac{16}{47}\right)$$ $$e\left(\frac{14}{1269}\right)$$ $$e\left(\frac{701}{1269}\right)$$ $$e\left(\frac{245}{423}\right)$$ $$e\left(\frac{128}{423}\right)$$ $$e\left(\frac{254}{1269}\right)$$ $$e\left(\frac{493}{1269}\right)$$
$$\chi_{5077}(13,\cdot)$$ 5077.v 1692 yes $$-1$$ $$1$$ $$e\left(\frac{721}{1692}\right)$$ $$e\left(\frac{211}{282}\right)$$ $$e\left(\frac{721}{846}\right)$$ $$e\left(\frac{105}{188}\right)$$ $$e\left(\frac{295}{1692}\right)$$ $$e\left(\frac{271}{423}\right)$$ $$e\left(\frac{157}{564}\right)$$ $$e\left(\frac{70}{141}\right)$$ $$e\left(\frac{833}{846}\right)$$ $$e\left(\frac{629}{1692}\right)$$
$$\chi_{5077}(14,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{1373}{5076}\right)$$ $$e\left(\frac{737}{846}\right)$$ $$e\left(\frac{1373}{2538}\right)$$ $$e\left(\frac{63}{188}\right)$$ $$e\left(\frac{719}{5076}\right)$$ $$e\left(\frac{140}{1269}\right)$$ $$e\left(\frac{1373}{1692}\right)$$ $$e\left(\frac{314}{423}\right)$$ $$e\left(\frac{1537}{2538}\right)$$ $$e\left(\frac{2749}{5076}\right)$$
$$\chi_{5077}(15,\cdot)$$ 5077.v 1692 yes $$-1$$ $$1$$ $$e\left(\frac{1553}{1692}\right)$$ $$e\left(\frac{185}{282}\right)$$ $$e\left(\frac{707}{846}\right)$$ $$e\left(\frac{113}{188}\right)$$ $$e\left(\frac{971}{1692}\right)$$ $$e\left(\frac{122}{423}\right)$$ $$e\left(\frac{425}{564}\right)$$ $$e\left(\frac{44}{141}\right)$$ $$e\left(\frac{439}{846}\right)$$ $$e\left(\frac{625}{1692}\right)$$
$$\chi_{5077}(16,\cdot)$$ 5077.u 1269 yes $$1$$ $$1$$ $$e\left(\frac{1}{1269}\right)$$ $$e\left(\frac{185}{423}\right)$$ $$e\left(\frac{2}{1269}\right)$$ $$e\left(\frac{11}{47}\right)$$ $$e\left(\frac{556}{1269}\right)$$ $$e\left(\frac{103}{1269}\right)$$ $$e\left(\frac{1}{423}\right)$$ $$e\left(\frac{370}{423}\right)$$ $$e\left(\frac{298}{1269}\right)$$ $$e\left(\frac{1088}{1269}\right)$$
$$\chi_{5077}(17,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{3697}{5076}\right)$$ $$e\left(\frac{823}{846}\right)$$ $$e\left(\frac{1159}{2538}\right)$$ $$e\left(\frac{59}{188}\right)$$ $$e\left(\frac{3559}{5076}\right)$$ $$e\left(\frac{340}{1269}\right)$$ $$e\left(\frac{313}{1692}\right)$$ $$e\left(\frac{400}{423}\right)$$ $$e\left(\frac{107}{2538}\right)$$ $$e\left(\frac{3413}{5076}\right)$$
$$\chi_{5077}(18,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{3649}{5076}\right)$$ $$e\left(\frac{613}{846}\right)$$ $$e\left(\frac{1111}{2538}\right)$$ $$e\left(\frac{95}{188}\right)$$ $$e\left(\frac{2251}{5076}\right)$$ $$e\left(\frac{373}{1269}\right)$$ $$e\left(\frac{265}{1692}\right)$$ $$e\left(\frac{190}{423}\right)$$ $$e\left(\frac{569}{2538}\right)$$ $$e\left(\frac{1949}{5076}\right)$$
$$\chi_{5077}(19,\cdot)$$ 5077.w 2538 yes $$1$$ $$1$$ $$e\left(\frac{2455}{2538}\right)$$ $$e\left(\frac{148}{423}\right)$$ $$e\left(\frac{1186}{1269}\right)$$ $$e\left(\frac{27}{94}\right)$$ $$e\left(\frac{805}{2538}\right)$$ $$e\left(\frac{167}{1269}\right)$$ $$e\left(\frac{763}{846}\right)$$ $$e\left(\frac{296}{423}\right)$$ $$e\left(\frac{323}{1269}\right)$$ $$e\left(\frac{2333}{2538}\right)$$
$$\chi_{5077}(20,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{299}{5076}\right)$$ $$e\left(\frac{797}{846}\right)$$ $$e\left(\frac{299}{2538}\right)$$ $$e\left(\frac{93}{188}\right)$$ $$e\left(\frac{5}{5076}\right)$$ $$e\left(\frac{1037}{1269}\right)$$ $$e\left(\frac{299}{1692}\right)$$ $$e\left(\frac{374}{423}\right)$$ $$e\left(\frac{1405}{2538}\right)$$ $$e\left(\frac{4255}{5076}\right)$$
$$\chi_{5077}(21,\cdot)$$ 5077.l 54 yes $$1$$ $$1$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$-1$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{29}{54}\right)$$
$$\chi_{5077}(22,\cdot)$$ 5077.q 282 yes $$1$$ $$1$$ $$e\left(\frac{131}{282}\right)$$ $$e\left(\frac{15}{47}\right)$$ $$e\left(\frac{131}{141}\right)$$ $$e\left(\frac{91}{94}\right)$$ $$e\left(\frac{221}{282}\right)$$ $$e\left(\frac{49}{141}\right)$$ $$e\left(\frac{37}{94}\right)$$ $$e\left(\frac{30}{47}\right)$$ $$e\left(\frac{61}{141}\right)$$ $$e\left(\frac{259}{282}\right)$$
$$\chi_{5077}(23,\cdot)$$ 5077.v 1692 yes $$-1$$ $$1$$ $$e\left(\frac{1193}{1692}\right)$$ $$e\left(\frac{161}{282}\right)$$ $$e\left(\frac{347}{846}\right)$$ $$e\left(\frac{77}{188}\right)$$ $$e\left(\frac{467}{1692}\right)$$ $$e\left(\frac{158}{423}\right)$$ $$e\left(\frac{65}{564}\right)$$ $$e\left(\frac{20}{141}\right)$$ $$e\left(\frac{97}{846}\right)$$ $$e\left(\frac{1489}{1692}\right)$$
$$\chi_{5077}(24,\cdot)$$ 5077.s 564 yes $$-1$$ $$1$$ $$e\left(\frac{485}{564}\right)$$ $$e\left(\frac{1}{94}\right)$$ $$e\left(\frac{203}{282}\right)$$ $$e\left(\frac{75}{188}\right)$$ $$e\left(\frac{491}{564}\right)$$ $$e\left(\frac{116}{141}\right)$$ $$e\left(\frac{109}{188}\right)$$ $$e\left(\frac{1}{47}\right)$$ $$e\left(\frac{73}{282}\right)$$ $$e\left(\frac{481}{564}\right)$$
$$\chi_{5077}(25,\cdot)$$ 5077.m 94 yes $$1$$ $$1$$ $$e\left(\frac{11}{94}\right)$$ $$e\left(\frac{21}{47}\right)$$ $$e\left(\frac{11}{47}\right)$$ $$e\left(\frac{71}{94}\right)$$ $$e\left(\frac{53}{94}\right)$$ $$e\left(\frac{26}{47}\right)$$ $$e\left(\frac{33}{94}\right)$$ $$e\left(\frac{42}{47}\right)$$ $$e\left(\frac{41}{47}\right)$$ $$e\left(\frac{77}{94}\right)$$
$$\chi_{5077}(26,\cdot)$$ 5077.u 1269 yes $$1$$ $$1$$ $$e\left(\frac{541}{1269}\right)$$ $$e\left(\frac{257}{423}\right)$$ $$e\left(\frac{1082}{1269}\right)$$ $$e\left(\frac{29}{47}\right)$$ $$e\left(\frac{43}{1269}\right)$$ $$e\left(\frac{1156}{1269}\right)$$ $$e\left(\frac{118}{423}\right)$$ $$e\left(\frac{91}{423}\right)$$ $$e\left(\frac{55}{1269}\right)$$ $$e\left(\frac{1061}{1269}\right)$$
$$\chi_{5077}(27,\cdot)$$ 5077.q 282 yes $$1$$ $$1$$ $$e\left(\frac{163}{282}\right)$$ $$e\left(\frac{14}{47}\right)$$ $$e\left(\frac{22}{141}\right)$$ $$e\left(\frac{63}{94}\right)$$ $$e\left(\frac{247}{282}\right)$$ $$e\left(\frac{5}{141}\right)$$ $$e\left(\frac{69}{94}\right)$$ $$e\left(\frac{28}{47}\right)$$ $$e\left(\frac{35}{141}\right)$$ $$e\left(\frac{107}{282}\right)$$
$$\chi_{5077}(28,\cdot)$$ 5077.t 846 yes $$1$$ $$1$$ $$e\left(\frac{229}{846}\right)$$ $$e\left(\frac{103}{141}\right)$$ $$e\left(\frac{229}{423}\right)$$ $$e\left(\frac{37}{94}\right)$$ $$e\left(\frac{1}{846}\right)$$ $$e\left(\frac{161}{423}\right)$$ $$e\left(\frac{229}{282}\right)$$ $$e\left(\frac{65}{141}\right)$$ $$e\left(\frac{281}{423}\right)$$ $$e\left(\frac{5}{846}\right)$$
$$\chi_{5077}(29,\cdot)$$ 5077.v 1692 yes $$-1$$ $$1$$ $$e\left(\frac{191}{1692}\right)$$ $$e\left(\frac{113}{282}\right)$$ $$e\left(\frac{191}{846}\right)$$ $$e\left(\frac{99}{188}\right)$$ $$e\left(\frac{869}{1692}\right)$$ $$e\left(\frac{371}{423}\right)$$ $$e\left(\frac{191}{564}\right)$$ $$e\left(\frac{113}{141}\right)$$ $$e\left(\frac{541}{846}\right)$$ $$e\left(\frac{115}{1692}\right)$$
$$\chi_{5077}(30,\cdot)$$ 5077.u 1269 yes $$1$$ $$1$$ $$e\left(\frac{1165}{1269}\right)$$ $$e\left(\frac{218}{423}\right)$$ $$e\left(\frac{1061}{1269}\right)$$ $$e\left(\frac{31}{47}\right)$$ $$e\left(\frac{550}{1269}\right)$$ $$e\left(\frac{709}{1269}\right)$$ $$e\left(\frac{319}{423}\right)$$ $$e\left(\frac{13}{423}\right)$$ $$e\left(\frac{733}{1269}\right)$$ $$e\left(\frac{1058}{1269}\right)$$
$$\chi_{5077}(31,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{2971}{5076}\right)$$ $$e\left(\frac{79}{846}\right)$$ $$e\left(\frac{433}{2538}\right)$$ $$e\left(\frac{157}{188}\right)$$ $$e\left(\frac{3445}{5076}\right)$$ $$e\left(\frac{46}{1269}\right)$$ $$e\left(\frac{1279}{1692}\right)$$ $$e\left(\frac{79}{423}\right)$$ $$e\left(\frac{1067}{2538}\right)$$ $$e\left(\frac{2843}{5076}\right)$$
$$\chi_{5077}(32,\cdot)$$ 5077.x 5076 yes $$-1$$ $$1$$ $$e\left(\frac{5}{5076}\right)$$ $$e\left(\frac{251}{846}\right)$$ $$e\left(\frac{5}{2538}\right)$$ $$e\left(\frac{55}{188}\right)$$ $$e\left(\frac{1511}{5076}\right)$$ $$e\left(\frac{446}{1269}\right)$$ $$e\left(\frac{5}{1692}\right)$$ $$e\left(\frac{251}{423}\right)$$ $$e\left(\frac{745}{2538}\right)$$ $$e\left(\frac{1633}{5076}\right)$$