Properties

Modulus $8049$
Structure \(C_{2}\times C_{2682}\)
Order $5364$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(8049)
 
pari: g = idealstar(,8049,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 5364
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2682}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{8049}(2684,\cdot)$, $\chi_{8049}(5368,\cdot)$

First 32 of 5364 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{8049}(1,\cdot)\) 8049.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8049}(2,\cdot)\) 8049.w 2682 yes \(1\) \(1\) \(e\left(\frac{671}{1341}\right)\) \(e\left(\frac{1}{1341}\right)\) \(e\left(\frac{415}{1341}\right)\) \(e\left(\frac{863}{894}\right)\) \(e\left(\frac{224}{447}\right)\) \(e\left(\frac{362}{447}\right)\) \(e\left(\frac{1615}{2682}\right)\) \(e\left(\frac{269}{298}\right)\) \(e\left(\frac{1249}{2682}\right)\) \(e\left(\frac{2}{1341}\right)\)
\(\chi_{8049}(4,\cdot)\) 8049.u 1341 no \(1\) \(1\) \(e\left(\frac{1}{1341}\right)\) \(e\left(\frac{2}{1341}\right)\) \(e\left(\frac{830}{1341}\right)\) \(e\left(\frac{416}{447}\right)\) \(e\left(\frac{1}{447}\right)\) \(e\left(\frac{277}{447}\right)\) \(e\left(\frac{274}{1341}\right)\) \(e\left(\frac{120}{149}\right)\) \(e\left(\frac{1249}{1341}\right)\) \(e\left(\frac{4}{1341}\right)\)
\(\chi_{8049}(5,\cdot)\) 8049.w 2682 yes \(1\) \(1\) \(e\left(\frac{415}{1341}\right)\) \(e\left(\frac{830}{1341}\right)\) \(e\left(\frac{1154}{1341}\right)\) \(e\left(\frac{643}{894}\right)\) \(e\left(\frac{415}{447}\right)\) \(e\left(\frac{76}{447}\right)\) \(e\left(\frac{791}{2682}\right)\) \(e\left(\frac{217}{298}\right)\) \(e\left(\frac{77}{2682}\right)\) \(e\left(\frac{319}{1341}\right)\)
\(\chi_{8049}(7,\cdot)\) 8049.s 894 no \(-1\) \(1\) \(e\left(\frac{863}{894}\right)\) \(e\left(\frac{416}{447}\right)\) \(e\left(\frac{643}{894}\right)\) \(e\left(\frac{67}{298}\right)\) \(e\left(\frac{267}{298}\right)\) \(e\left(\frac{102}{149}\right)\) \(e\left(\frac{223}{447}\right)\) \(e\left(\frac{15}{298}\right)\) \(e\left(\frac{85}{447}\right)\) \(e\left(\frac{385}{447}\right)\)
\(\chi_{8049}(8,\cdot)\) 8049.t 894 yes \(1\) \(1\) \(e\left(\frac{224}{447}\right)\) \(e\left(\frac{1}{447}\right)\) \(e\left(\frac{415}{447}\right)\) \(e\left(\frac{267}{298}\right)\) \(e\left(\frac{75}{149}\right)\) \(e\left(\frac{64}{149}\right)\) \(e\left(\frac{721}{894}\right)\) \(e\left(\frac{211}{298}\right)\) \(e\left(\frac{355}{894}\right)\) \(e\left(\frac{2}{447}\right)\)
\(\chi_{8049}(10,\cdot)\) 8049.q 447 no \(1\) \(1\) \(e\left(\frac{362}{447}\right)\) \(e\left(\frac{277}{447}\right)\) \(e\left(\frac{76}{447}\right)\) \(e\left(\frac{102}{149}\right)\) \(e\left(\frac{64}{149}\right)\) \(e\left(\frac{146}{149}\right)\) \(e\left(\frac{401}{447}\right)\) \(e\left(\frac{94}{149}\right)\) \(e\left(\frac{221}{447}\right)\) \(e\left(\frac{107}{447}\right)\)
\(\chi_{8049}(11,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{1615}{2682}\right)\) \(e\left(\frac{274}{1341}\right)\) \(e\left(\frac{791}{2682}\right)\) \(e\left(\frac{223}{447}\right)\) \(e\left(\frac{721}{894}\right)\) \(e\left(\frac{401}{447}\right)\) \(e\left(\frac{1321}{2682}\right)\) \(e\left(\frac{50}{149}\right)\) \(e\left(\frac{271}{2682}\right)\) \(e\left(\frac{548}{1341}\right)\)
\(\chi_{8049}(13,\cdot)\) 8049.p 298 no \(-1\) \(1\) \(e\left(\frac{269}{298}\right)\) \(e\left(\frac{120}{149}\right)\) \(e\left(\frac{217}{298}\right)\) \(e\left(\frac{15}{298}\right)\) \(e\left(\frac{211}{298}\right)\) \(e\left(\frac{94}{149}\right)\) \(e\left(\frac{50}{149}\right)\) \(e\left(\frac{119}{298}\right)\) \(e\left(\frac{142}{149}\right)\) \(e\left(\frac{91}{149}\right)\)
\(\chi_{8049}(14,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{1249}{2682}\right)\) \(e\left(\frac{1249}{1341}\right)\) \(e\left(\frac{77}{2682}\right)\) \(e\left(\frac{85}{447}\right)\) \(e\left(\frac{355}{894}\right)\) \(e\left(\frac{221}{447}\right)\) \(e\left(\frac{271}{2682}\right)\) \(e\left(\frac{142}{149}\right)\) \(e\left(\frac{1759}{2682}\right)\) \(e\left(\frac{1157}{1341}\right)\)
\(\chi_{8049}(16,\cdot)\) 8049.u 1341 no \(1\) \(1\) \(e\left(\frac{2}{1341}\right)\) \(e\left(\frac{4}{1341}\right)\) \(e\left(\frac{319}{1341}\right)\) \(e\left(\frac{385}{447}\right)\) \(e\left(\frac{2}{447}\right)\) \(e\left(\frac{107}{447}\right)\) \(e\left(\frac{548}{1341}\right)\) \(e\left(\frac{91}{149}\right)\) \(e\left(\frac{1157}{1341}\right)\) \(e\left(\frac{8}{1341}\right)\)
\(\chi_{8049}(17,\cdot)\) 8049.n 298 yes \(1\) \(1\) \(e\left(\frac{96}{149}\right)\) \(e\left(\frac{43}{149}\right)\) \(e\left(\frac{114}{149}\right)\) \(e\left(\frac{173}{298}\right)\) \(e\left(\frac{139}{149}\right)\) \(e\left(\frac{61}{149}\right)\) \(e\left(\frac{11}{298}\right)\) \(e\left(\frac{101}{298}\right)\) \(e\left(\frac{67}{298}\right)\) \(e\left(\frac{86}{149}\right)\)
\(\chi_{8049}(19,\cdot)\) 8049.s 894 no \(-1\) \(1\) \(e\left(\frac{125}{894}\right)\) \(e\left(\frac{125}{447}\right)\) \(e\left(\frac{493}{894}\right)\) \(e\left(\frac{297}{298}\right)\) \(e\left(\frac{125}{298}\right)\) \(e\left(\frac{103}{149}\right)\) \(e\left(\frac{139}{447}\right)\) \(e\left(\frac{151}{298}\right)\) \(e\left(\frac{61}{447}\right)\) \(e\left(\frac{250}{447}\right)\)
\(\chi_{8049}(20,\cdot)\) 8049.w 2682 yes \(1\) \(1\) \(e\left(\frac{416}{1341}\right)\) \(e\left(\frac{832}{1341}\right)\) \(e\left(\frac{643}{1341}\right)\) \(e\left(\frac{581}{894}\right)\) \(e\left(\frac{416}{447}\right)\) \(e\left(\frac{353}{447}\right)\) \(e\left(\frac{1339}{2682}\right)\) \(e\left(\frac{159}{298}\right)\) \(e\left(\frac{2575}{2682}\right)\) \(e\left(\frac{323}{1341}\right)\)
\(\chi_{8049}(22,\cdot)\) 8049.v 2682 no \(-1\) \(1\) \(e\left(\frac{275}{2682}\right)\) \(e\left(\frac{275}{1341}\right)\) \(e\left(\frac{1621}{2682}\right)\) \(e\left(\frac{415}{894}\right)\) \(e\left(\frac{275}{894}\right)\) \(e\left(\frac{316}{447}\right)\) \(e\left(\frac{127}{1341}\right)\) \(e\left(\frac{71}{298}\right)\) \(e\left(\frac{760}{1341}\right)\) \(e\left(\frac{550}{1341}\right)\)
\(\chi_{8049}(23,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{2455}{2682}\right)\) \(e\left(\frac{1114}{1341}\right)\) \(e\left(\frac{671}{2682}\right)\) \(e\left(\frac{166}{447}\right)\) \(e\left(\frac{667}{894}\right)\) \(e\left(\frac{74}{447}\right)\) \(e\left(\frac{829}{2682}\right)\) \(e\left(\frac{88}{149}\right)\) \(e\left(\frac{769}{2682}\right)\) \(e\left(\frac{887}{1341}\right)\)
\(\chi_{8049}(25,\cdot)\) 8049.u 1341 no \(1\) \(1\) \(e\left(\frac{830}{1341}\right)\) \(e\left(\frac{319}{1341}\right)\) \(e\left(\frac{967}{1341}\right)\) \(e\left(\frac{196}{447}\right)\) \(e\left(\frac{383}{447}\right)\) \(e\left(\frac{152}{447}\right)\) \(e\left(\frac{791}{1341}\right)\) \(e\left(\frac{68}{149}\right)\) \(e\left(\frac{77}{1341}\right)\) \(e\left(\frac{638}{1341}\right)\)
\(\chi_{8049}(26,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{1081}{2682}\right)\) \(e\left(\frac{1081}{1341}\right)\) \(e\left(\frac{101}{2682}\right)\) \(e\left(\frac{7}{447}\right)\) \(e\left(\frac{187}{894}\right)\) \(e\left(\frac{197}{447}\right)\) \(e\left(\frac{2515}{2682}\right)\) \(e\left(\frac{45}{149}\right)\) \(e\left(\frac{1123}{2682}\right)\) \(e\left(\frac{821}{1341}\right)\)
\(\chi_{8049}(28,\cdot)\) 8049.v 2682 no \(-1\) \(1\) \(e\left(\frac{2591}{2682}\right)\) \(e\left(\frac{1250}{1341}\right)\) \(e\left(\frac{907}{2682}\right)\) \(e\left(\frac{139}{894}\right)\) \(e\left(\frac{803}{894}\right)\) \(e\left(\frac{136}{447}\right)\) \(e\left(\frac{943}{1341}\right)\) \(e\left(\frac{255}{298}\right)\) \(e\left(\frac{163}{1341}\right)\) \(e\left(\frac{1159}{1341}\right)\)
\(\chi_{8049}(29,\cdot)\) 8049.n 298 yes \(1\) \(1\) \(e\left(\frac{35}{149}\right)\) \(e\left(\frac{70}{149}\right)\) \(e\left(\frac{144}{149}\right)\) \(e\left(\frac{195}{298}\right)\) \(e\left(\frac{105}{149}\right)\) \(e\left(\frac{30}{149}\right)\) \(e\left(\frac{257}{298}\right)\) \(e\left(\frac{57}{298}\right)\) \(e\left(\frac{265}{298}\right)\) \(e\left(\frac{140}{149}\right)\)
\(\chi_{8049}(31,\cdot)\) 8049.m 149 no \(1\) \(1\) \(e\left(\frac{58}{149}\right)\) \(e\left(\frac{116}{149}\right)\) \(e\left(\frac{13}{149}\right)\) \(e\left(\frac{119}{149}\right)\) \(e\left(\frac{25}{149}\right)\) \(e\left(\frac{71}{149}\right)\) \(e\left(\frac{98}{149}\right)\) \(e\left(\frac{60}{149}\right)\) \(e\left(\frac{28}{149}\right)\) \(e\left(\frac{83}{149}\right)\)
\(\chi_{8049}(32,\cdot)\) 8049.w 2682 yes \(1\) \(1\) \(e\left(\frac{673}{1341}\right)\) \(e\left(\frac{5}{1341}\right)\) \(e\left(\frac{734}{1341}\right)\) \(e\left(\frac{739}{894}\right)\) \(e\left(\frac{226}{447}\right)\) \(e\left(\frac{22}{447}\right)\) \(e\left(\frac{29}{2682}\right)\) \(e\left(\frac{153}{298}\right)\) \(e\left(\frac{881}{2682}\right)\) \(e\left(\frac{10}{1341}\right)\)
\(\chi_{8049}(34,\cdot)\) 8049.u 1341 no \(1\) \(1\) \(e\left(\frac{194}{1341}\right)\) \(e\left(\frac{388}{1341}\right)\) \(e\left(\frac{100}{1341}\right)\) \(e\left(\frac{244}{447}\right)\) \(e\left(\frac{194}{447}\right)\) \(e\left(\frac{98}{447}\right)\) \(e\left(\frac{857}{1341}\right)\) \(e\left(\frac{36}{149}\right)\) \(e\left(\frac{926}{1341}\right)\) \(e\left(\frac{776}{1341}\right)\)
\(\chi_{8049}(35,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{737}{2682}\right)\) \(e\left(\frac{737}{1341}\right)\) \(e\left(\frac{1555}{2682}\right)\) \(e\left(\frac{422}{447}\right)\) \(e\left(\frac{737}{894}\right)\) \(e\left(\frac{382}{447}\right)\) \(e\left(\frac{2129}{2682}\right)\) \(e\left(\frac{116}{149}\right)\) \(e\left(\frac{587}{2682}\right)\) \(e\left(\frac{133}{1341}\right)\)
\(\chi_{8049}(37,\cdot)\) 8049.v 2682 no \(-1\) \(1\) \(e\left(\frac{2563}{2682}\right)\) \(e\left(\frac{1222}{1341}\right)\) \(e\left(\frac{1805}{2682}\right)\) \(e\left(\frac{113}{894}\right)\) \(e\left(\frac{775}{894}\right)\) \(e\left(\frac{281}{447}\right)\) \(e\left(\frac{1130}{1341}\right)\) \(e\left(\frac{173}{298}\right)\) \(e\left(\frac{110}{1341}\right)\) \(e\left(\frac{1103}{1341}\right)\)
\(\chi_{8049}(38,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{1717}{2682}\right)\) \(e\left(\frac{376}{1341}\right)\) \(e\left(\frac{2309}{2682}\right)\) \(e\left(\frac{430}{447}\right)\) \(e\left(\frac{823}{894}\right)\) \(e\left(\frac{224}{447}\right)\) \(e\left(\frac{2449}{2682}\right)\) \(e\left(\frac{61}{149}\right)\) \(e\left(\frac{1615}{2682}\right)\) \(e\left(\frac{752}{1341}\right)\)
\(\chi_{8049}(40,\cdot)\) 8049.u 1341 no \(1\) \(1\) \(e\left(\frac{1087}{1341}\right)\) \(e\left(\frac{833}{1341}\right)\) \(e\left(\frac{1058}{1341}\right)\) \(e\left(\frac{275}{447}\right)\) \(e\left(\frac{193}{447}\right)\) \(e\left(\frac{268}{447}\right)\) \(e\left(\frac{136}{1341}\right)\) \(e\left(\frac{65}{149}\right)\) \(e\left(\frac{571}{1341}\right)\) \(e\left(\frac{325}{1341}\right)\)
\(\chi_{8049}(41,\cdot)\) 8049.x 2682 yes \(-1\) \(1\) \(e\left(\frac{2605}{2682}\right)\) \(e\left(\frac{1264}{1341}\right)\) \(e\left(\frac{1799}{2682}\right)\) \(e\left(\frac{76}{447}\right)\) \(e\left(\frac{817}{894}\right)\) \(e\left(\frac{287}{447}\right)\) \(e\left(\frac{1699}{2682}\right)\) \(e\left(\frac{148}{149}\right)\) \(e\left(\frac{379}{2682}\right)\) \(e\left(\frac{1187}{1341}\right)\)
\(\chi_{8049}(43,\cdot)\) 8049.v 2682 no \(-1\) \(1\) \(e\left(\frac{683}{2682}\right)\) \(e\left(\frac{683}{1341}\right)\) \(e\left(\frac{2329}{2682}\right)\) \(e\left(\frac{283}{894}\right)\) \(e\left(\frac{683}{894}\right)\) \(e\left(\frac{55}{447}\right)\) \(e\left(\frac{1042}{1341}\right)\) \(e\left(\frac{159}{298}\right)\) \(e\left(\frac{766}{1341}\right)\) \(e\left(\frac{25}{1341}\right)\)
\(\chi_{8049}(44,\cdot)\) 8049.r 894 yes \(-1\) \(1\) \(e\left(\frac{539}{894}\right)\) \(e\left(\frac{92}{447}\right)\) \(e\left(\frac{817}{894}\right)\) \(e\left(\frac{64}{149}\right)\) \(e\left(\frac{241}{298}\right)\) \(e\left(\frac{77}{149}\right)\) \(e\left(\frac{623}{894}\right)\) \(e\left(\frac{21}{149}\right)\) \(e\left(\frac{29}{894}\right)\) \(e\left(\frac{184}{447}\right)\)
\(\chi_{8049}(46,\cdot)\) 8049.v 2682 no \(-1\) \(1\) \(e\left(\frac{1115}{2682}\right)\) \(e\left(\frac{1115}{1341}\right)\) \(e\left(\frac{1501}{2682}\right)\) \(e\left(\frac{301}{894}\right)\) \(e\left(\frac{221}{894}\right)\) \(e\left(\frac{436}{447}\right)\) \(e\left(\frac{1222}{1341}\right)\) \(e\left(\frac{147}{298}\right)\) \(e\left(\frac{1009}{1341}\right)\) \(e\left(\frac{889}{1341}\right)\)
\(\chi_{8049}(47,\cdot)\) 8049.w 2682 yes \(1\) \(1\) \(e\left(\frac{26}{1341}\right)\) \(e\left(\frac{52}{1341}\right)\) \(e\left(\frac{124}{1341}\right)\) \(e\left(\frac{623}{894}\right)\) \(e\left(\frac{26}{447}\right)\) \(e\left(\frac{50}{447}\right)\) \(e\left(\frac{2179}{2682}\right)\) \(e\left(\frac{131}{298}\right)\) \(e\left(\frac{1921}{2682}\right)\) \(e\left(\frac{104}{1341}\right)\)
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