Properties

Modulus $6815$
Structure \(C_{644}\times C_{4}\times C_{2}\)
Order $5152$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(6815)
 
pari: g = idealstar(,6815,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 5152
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{644}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6815}(2727,\cdot)$, $\chi_{6815}(2351,\cdot)$, $\chi_{6815}(146,\cdot)$

First 32 of 5152 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{6815}(1,\cdot)\) 6815.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6815}(2,\cdot)\) 6815.da 644 yes \(1\) \(1\) \(e\left(\frac{53}{161}\right)\) \(e\left(\frac{243}{322}\right)\) \(e\left(\frac{106}{161}\right)\) \(e\left(\frac{27}{322}\right)\) \(e\left(\frac{129}{644}\right)\) \(e\left(\frac{159}{161}\right)\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{407}{644}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{449}{644}\right)\)
\(\chi_{6815}(3,\cdot)\) 6815.cr 644 yes \(1\) \(1\) \(e\left(\frac{243}{322}\right)\) \(e\left(\frac{135}{161}\right)\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{191}{322}\right)\) \(e\left(\frac{519}{644}\right)\) \(e\left(\frac{85}{322}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{327}{644}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{159}{644}\right)\)
\(\chi_{6815}(4,\cdot)\) 6815.cn 322 yes \(1\) \(1\) \(e\left(\frac{106}{161}\right)\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{27}{161}\right)\) \(e\left(\frac{129}{322}\right)\) \(e\left(\frac{157}{161}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{85}{322}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{127}{322}\right)\)
\(\chi_{6815}(6,\cdot)\) 6815.cl 322 no \(1\) \(1\) \(e\left(\frac{27}{322}\right)\) \(e\left(\frac{191}{322}\right)\) \(e\left(\frac{27}{161}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{1}{161}\right)\) \(e\left(\frac{81}{322}\right)\) \(e\left(\frac{30}{161}\right)\) \(e\left(\frac{45}{322}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{152}{161}\right)\)
\(\chi_{6815}(7,\cdot)\) 6815.cy 644 yes \(-1\) \(1\) \(e\left(\frac{129}{644}\right)\) \(e\left(\frac{519}{644}\right)\) \(e\left(\frac{129}{322}\right)\) \(e\left(\frac{1}{161}\right)\) \(e\left(\frac{421}{644}\right)\) \(e\left(\frac{387}{644}\right)\) \(e\left(\frac{197}{322}\right)\) \(e\left(\frac{94}{161}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{75}{644}\right)\)
\(\chi_{6815}(8,\cdot)\) 6815.da 644 yes \(1\) \(1\) \(e\left(\frac{159}{161}\right)\) \(e\left(\frac{85}{322}\right)\) \(e\left(\frac{157}{161}\right)\) \(e\left(\frac{81}{322}\right)\) \(e\left(\frac{387}{644}\right)\) \(e\left(\frac{155}{161}\right)\) \(e\left(\frac{85}{161}\right)\) \(e\left(\frac{577}{644}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{59}{644}\right)\)
\(\chi_{6815}(9,\cdot)\) 6815.cn 322 yes \(1\) \(1\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{30}{161}\right)\) \(e\left(\frac{197}{322}\right)\) \(e\left(\frac{85}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{5}{322}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{159}{322}\right)\)
\(\chi_{6815}(11,\cdot)\) 6815.cv 644 no \(1\) \(1\) \(e\left(\frac{407}{644}\right)\) \(e\left(\frac{327}{644}\right)\) \(e\left(\frac{85}{322}\right)\) \(e\left(\frac{45}{322}\right)\) \(e\left(\frac{94}{161}\right)\) \(e\left(\frac{577}{644}\right)\) \(e\left(\frac{5}{322}\right)\) \(e\left(\frac{249}{644}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{120}{161}\right)\)
\(\chi_{6815}(12,\cdot)\) 6815.cg 92 yes \(1\) \(1\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{59}{92}\right)\)
\(\chi_{6815}(13,\cdot)\) 6815.cz 644 yes \(1\) \(1\) \(e\left(\frac{449}{644}\right)\) \(e\left(\frac{159}{644}\right)\) \(e\left(\frac{127}{322}\right)\) \(e\left(\frac{152}{161}\right)\) \(e\left(\frac{75}{644}\right)\) \(e\left(\frac{59}{644}\right)\) \(e\left(\frac{159}{322}\right)\) \(e\left(\frac{120}{161}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{291}{644}\right)\)
\(\chi_{6815}(14,\cdot)\) 6815.ct 644 yes \(-1\) \(1\) \(e\left(\frac{341}{644}\right)\) \(e\left(\frac{361}{644}\right)\) \(e\left(\frac{19}{322}\right)\) \(e\left(\frac{29}{322}\right)\) \(e\left(\frac{275}{322}\right)\) \(e\left(\frac{379}{644}\right)\) \(e\left(\frac{39}{322}\right)\) \(e\left(\frac{139}{644}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{131}{161}\right)\)
\(\chi_{6815}(16,\cdot)\) 6815.ci 161 no \(1\) \(1\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{102}{161}\right)\) \(e\left(\frac{54}{161}\right)\) \(e\left(\frac{129}{161}\right)\) \(e\left(\frac{153}{161}\right)\) \(e\left(\frac{6}{161}\right)\) \(e\left(\frac{85}{161}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{127}{161}\right)\)
\(\chi_{6815}(17,\cdot)\) 6815.bx 92 yes \(1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{7}{92}\right)\)
\(\chi_{6815}(18,\cdot)\) 6815.da 644 yes \(1\) \(1\) \(e\left(\frac{135}{161}\right)\) \(e\left(\frac{139}{322}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{87}{322}\right)\) \(e\left(\frac{523}{644}\right)\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{139}{161}\right)\) \(e\left(\frac{417}{644}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{123}{644}\right)\)
\(\chi_{6815}(19,\cdot)\) 6815.cs 644 yes \(1\) \(1\) \(e\left(\frac{277}{644}\right)\) \(e\left(\frac{433}{644}\right)\) \(e\left(\frac{277}{322}\right)\) \(e\left(\frac{33}{322}\right)\) \(e\left(\frac{213}{322}\right)\) \(e\left(\frac{187}{644}\right)\) \(e\left(\frac{111}{322}\right)\) \(e\left(\frac{569}{644}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{15}{322}\right)\)
\(\chi_{6815}(21,\cdot)\) 6815.cu 644 no \(-1\) \(1\) \(e\left(\frac{615}{644}\right)\) \(e\left(\frac{415}{644}\right)\) \(e\left(\frac{293}{322}\right)\) \(e\left(\frac{193}{322}\right)\) \(e\left(\frac{74}{161}\right)\) \(e\left(\frac{557}{644}\right)\) \(e\left(\frac{93}{322}\right)\) \(e\left(\frac{59}{644}\right)\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{117}{322}\right)\)
\(\chi_{6815}(22,\cdot)\) 6815.cz 644 yes \(1\) \(1\) \(e\left(\frac{619}{644}\right)\) \(e\left(\frac{169}{644}\right)\) \(e\left(\frac{297}{322}\right)\) \(e\left(\frac{36}{161}\right)\) \(e\left(\frac{505}{644}\right)\) \(e\left(\frac{569}{644}\right)\) \(e\left(\frac{169}{322}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{285}{644}\right)\)
\(\chi_{6815}(23,\cdot)\) 6815.cw 644 yes \(1\) \(1\) \(e\left(\frac{271}{644}\right)\) \(e\left(\frac{641}{644}\right)\) \(e\left(\frac{271}{322}\right)\) \(e\left(\frac{67}{161}\right)\) \(e\left(\frac{515}{644}\right)\) \(e\left(\frac{169}{644}\right)\) \(e\left(\frac{319}{322}\right)\) \(e\left(\frac{199}{322}\right)\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{195}{644}\right)\)
\(\chi_{6815}(24,\cdot)\) 6815.ck 322 yes \(1\) \(1\) \(e\left(\frac{239}{322}\right)\) \(e\left(\frac{33}{322}\right)\) \(e\left(\frac{78}{161}\right)\) \(e\left(\frac{136}{161}\right)\) \(e\left(\frac{131}{322}\right)\) \(e\left(\frac{73}{322}\right)\) \(e\left(\frac{33}{161}\right)\) \(e\left(\frac{65}{161}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{109}{322}\right)\)
\(\chi_{6815}(26,\cdot)\) 6815.cv 644 no \(1\) \(1\) \(e\left(\frac{17}{644}\right)\) \(e\left(\frac{1}{644}\right)\) \(e\left(\frac{17}{322}\right)\) \(e\left(\frac{9}{322}\right)\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{51}{644}\right)\) \(e\left(\frac{1}{322}\right)\) \(e\left(\frac{243}{644}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{24}{161}\right)\)
\(\chi_{6815}(27,\cdot)\) 6815.cr 644 yes \(1\) \(1\) \(e\left(\frac{85}{322}\right)\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{85}{161}\right)\) \(e\left(\frac{251}{322}\right)\) \(e\left(\frac{269}{644}\right)\) \(e\left(\frac{255}{322}\right)\) \(e\left(\frac{5}{161}\right)\) \(e\left(\frac{337}{644}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{477}{644}\right)\)
\(\chi_{6815}(28,\cdot)\) 6815.ca 92 yes \(-1\) \(1\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{47}{92}\right)\)
\(\chi_{6815}(31,\cdot)\) 6815.cv 644 no \(1\) \(1\) \(e\left(\frac{135}{644}\right)\) \(e\left(\frac{311}{644}\right)\) \(e\left(\frac{135}{322}\right)\) \(e\left(\frac{223}{322}\right)\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{405}{644}\right)\) \(e\left(\frac{311}{322}\right)\) \(e\left(\frac{225}{644}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{58}{161}\right)\)
\(\chi_{6815}(32,\cdot)\) 6815.da 644 yes \(1\) \(1\) \(e\left(\frac{104}{161}\right)\) \(e\left(\frac{249}{322}\right)\) \(e\left(\frac{47}{161}\right)\) \(e\left(\frac{135}{322}\right)\) \(e\left(\frac{1}{644}\right)\) \(e\left(\frac{151}{161}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{103}{644}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{313}{644}\right)\)
\(\chi_{6815}(33,\cdot)\) 6815.cz 644 yes \(1\) \(1\) \(e\left(\frac{249}{644}\right)\) \(e\left(\frac{223}{644}\right)\) \(e\left(\frac{249}{322}\right)\) \(e\left(\frac{118}{161}\right)\) \(e\left(\frac{251}{644}\right)\) \(e\left(\frac{103}{644}\right)\) \(e\left(\frac{223}{322}\right)\) \(e\left(\frac{144}{161}\right)\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{639}{644}\right)\)
\(\chi_{6815}(34,\cdot)\) 6815.cn 322 yes \(1\) \(1\) \(e\left(\frac{95}{161}\right)\) \(e\left(\frac{34}{161}\right)\) \(e\left(\frac{29}{161}\right)\) \(e\left(\frac{129}{161}\right)\) \(e\left(\frac{187}{322}\right)\) \(e\left(\frac{124}{161}\right)\) \(e\left(\frac{68}{161}\right)\) \(e\left(\frac{263}{322}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{249}{322}\right)\)
\(\chi_{6815}(36,\cdot)\) 6815.ci 161 no \(1\) \(1\) \(e\left(\frac{27}{161}\right)\) \(e\left(\frac{30}{161}\right)\) \(e\left(\frac{54}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{2}{161}\right)\) \(e\left(\frac{81}{161}\right)\) \(e\left(\frac{60}{161}\right)\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{143}{161}\right)\)
\(\chi_{6815}(37,\cdot)\) 6815.cr 644 yes \(1\) \(1\) \(e\left(\frac{255}{322}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{94}{161}\right)\) \(e\left(\frac{109}{322}\right)\) \(e\left(\frac{485}{644}\right)\) \(e\left(\frac{121}{322}\right)\) \(e\left(\frac{15}{161}\right)\) \(e\left(\frac{45}{644}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{465}{644}\right)\)
\(\chi_{6815}(38,\cdot)\) 6815.cz 644 yes \(1\) \(1\) \(e\left(\frac{489}{644}\right)\) \(e\left(\frac{275}{644}\right)\) \(e\left(\frac{167}{322}\right)\) \(e\left(\frac{30}{161}\right)\) \(e\left(\frac{555}{644}\right)\) \(e\left(\frac{179}{644}\right)\) \(e\left(\frac{275}{322}\right)\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{479}{644}\right)\)
\(\chi_{6815}(39,\cdot)\) 6815.cs 644 yes \(1\) \(1\) \(e\left(\frac{291}{644}\right)\) \(e\left(\frac{55}{644}\right)\) \(e\left(\frac{291}{322}\right)\) \(e\left(\frac{173}{322}\right)\) \(e\left(\frac{297}{322}\right)\) \(e\left(\frac{229}{644}\right)\) \(e\left(\frac{55}{322}\right)\) \(e\left(\frac{163}{644}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{225}{322}\right)\)
\(\chi_{6815}(41,\cdot)\) 6815.cc 92 no \(1\) \(1\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{2}{23}\right)\)