Properties

Modulus 5077
Structure \(C_{5076}\)
Order 5076

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(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.

orbit label 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 \(-1\) \(1\) \(e\left(\frac{5}{5076}\right)\) \(e\left(\frac{251}{846}\right)\) \(e\left(\frac{5}{2538}\right)\) \(e\left(\frac{55}{188}\right)\) \(e\left(\frac{1511}{5076}\right)\) \(e\left(\frac{446}{1269}\right)\) \(e\left(\frac{5}{1692}\right)\) \(e\left(\frac{251}{423}\right)\) \(e\left(\frac{745}{2538}\right)\) \(e\left(\frac{1633}{5076}\right)\)