Properties

Modulus $4248$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{174}\)
Order $1392$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(4248)
 
pari: g = idealstar(,4248,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1392
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{174}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4248}(1063,\cdot)$, $\chi_{4248}(2125,\cdot)$, $\chi_{4248}(3305,\cdot)$, $\chi_{4248}(3601,\cdot)$

First 32 of 1392 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{4248}(1,\cdot)\) 4248.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4248}(5,\cdot)\) 4248.cl 174 yes \(-1\) \(1\) \(e\left(\frac{25}{87}\right)\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{80}{87}\right)\) \(e\left(\frac{143}{174}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{125}{174}\right)\) \(e\left(\frac{50}{87}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{64}{87}\right)\)
\(\chi_{4248}(7,\cdot)\) 4248.cg 174 no \(-1\) \(1\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{131}{174}\right)\) \(e\left(\frac{161}{174}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{85}{174}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{31}{87}\right)\) \(e\left(\frac{7}{174}\right)\)
\(\chi_{4248}(11,\cdot)\) 4248.ci 174 yes \(-1\) \(1\) \(e\left(\frac{80}{87}\right)\) \(e\left(\frac{161}{174}\right)\) \(e\left(\frac{82}{87}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{139}{174}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{83}{87}\right)\)
\(\chi_{4248}(13,\cdot)\) 4248.ce 174 yes \(-1\) \(1\) \(e\left(\frac{143}{174}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{7}{87}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{53}{174}\right)\) \(e\left(\frac{56}{87}\right)\) \(e\left(\frac{97}{174}\right)\) \(e\left(\frac{119}{174}\right)\)
\(\chi_{4248}(17,\cdot)\) 4248.bq 58 no \(-1\) \(1\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{23}{29}\right)\)
\(\chi_{4248}(19,\cdot)\) 4248.bt 58 no \(-1\) \(1\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{35}{58}\right)\)
\(\chi_{4248}(23,\cdot)\) 4248.bx 174 no \(-1\) \(1\) \(e\left(\frac{125}{174}\right)\) \(e\left(\frac{85}{174}\right)\) \(e\left(\frac{139}{174}\right)\) \(e\left(\frac{53}{174}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{95}{174}\right)\) \(e\left(\frac{38}{87}\right)\) \(e\left(\frac{13}{174}\right)\) \(e\left(\frac{73}{87}\right)\)
\(\chi_{4248}(25,\cdot)\) 4248.bw 87 no \(1\) \(1\) \(e\left(\frac{50}{87}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{56}{87}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{38}{87}\right)\) \(e\left(\frac{13}{87}\right)\) \(e\left(\frac{40}{87}\right)\) \(e\left(\frac{41}{87}\right)\)
\(\chi_{4248}(29,\cdot)\) 4248.cl 174 yes \(-1\) \(1\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{31}{87}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{97}{174}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{13}{174}\right)\) \(e\left(\frac{40}{87}\right)\) \(e\left(\frac{16}{87}\right)\) \(e\left(\frac{86}{87}\right)\)
\(\chi_{4248}(31,\cdot)\) 4248.ch 174 no \(1\) \(1\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{7}{174}\right)\) \(e\left(\frac{83}{87}\right)\) \(e\left(\frac{119}{174}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{41}{87}\right)\) \(e\left(\frac{86}{87}\right)\) \(e\left(\frac{49}{87}\right)\)
\(\chi_{4248}(35,\cdot)\) 4248.bn 58 no \(1\) \(1\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{45}{58}\right)\)
\(\chi_{4248}(37,\cdot)\) 4248.bo 58 no \(-1\) \(1\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{27}{58}\right)\)
\(\chi_{4248}(41,\cdot)\) 4248.cc 174 no \(-1\) \(1\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{59}{87}\right)\) \(e\left(\frac{151}{174}\right)\) \(e\left(\frac{46}{87}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{137}{174}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{103}{174}\right)\) \(e\left(\frac{43}{87}\right)\)
\(\chi_{4248}(43,\cdot)\) 4248.by 174 yes \(1\) \(1\) \(e\left(\frac{43}{174}\right)\) \(e\left(\frac{71}{174}\right)\) \(e\left(\frac{155}{174}\right)\) \(e\left(\frac{38}{87}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{32}{87}\right)\) \(e\left(\frac{43}{87}\right)\) \(e\left(\frac{17}{174}\right)\) \(e\left(\frac{62}{87}\right)\)
\(\chi_{4248}(47,\cdot)\) 4248.bx 174 no \(-1\) \(1\) \(e\left(\frac{37}{174}\right)\) \(e\left(\frac{53}{174}\right)\) \(e\left(\frac{101}{174}\right)\) \(e\left(\frac{31}{174}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{49}{174}\right)\) \(e\left(\frac{37}{87}\right)\) \(e\left(\frac{47}{174}\right)\) \(e\left(\frac{23}{87}\right)\)
\(\chi_{4248}(49,\cdot)\) 4248.bw 87 no \(1\) \(1\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{44}{87}\right)\) \(e\left(\frac{74}{87}\right)\) \(e\left(\frac{52}{87}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{68}{87}\right)\) \(e\left(\frac{62}{87}\right)\) \(e\left(\frac{7}{87}\right)\)
\(\chi_{4248}(53,\cdot)\) 4248.bh 58 no \(-1\) \(1\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{17}{29}\right)\)
\(\chi_{4248}(55,\cdot)\) 4248.bl 58 no \(1\) \(1\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{20}{29}\right)\)
\(\chi_{4248}(61,\cdot)\) 4248.ce 174 yes \(-1\) \(1\) \(e\left(\frac{163}{174}\right)\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{52}{87}\right)\) \(e\left(\frac{53}{87}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{103}{174}\right)\) \(e\left(\frac{76}{87}\right)\) \(e\left(\frac{113}{174}\right)\) \(e\left(\frac{31}{174}\right)\)
\(\chi_{4248}(65,\cdot)\) 4248.cd 174 no \(1\) \(1\) \(e\left(\frac{19}{174}\right)\) \(e\left(\frac{43}{87}\right)\) \(e\left(\frac{13}{87}\right)\) \(e\left(\frac{157}{174}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{2}{87}\right)\) \(e\left(\frac{19}{87}\right)\) \(e\left(\frac{137}{174}\right)\) \(e\left(\frac{73}{174}\right)\)
\(\chi_{4248}(67,\cdot)\) 4248.by 174 yes \(1\) \(1\) \(e\left(\frac{83}{174}\right)\) \(e\left(\frac{133}{174}\right)\) \(e\left(\frac{109}{174}\right)\) \(e\left(\frac{43}{87}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{82}{87}\right)\) \(e\left(\frac{83}{87}\right)\) \(e\left(\frac{49}{174}\right)\) \(e\left(\frac{61}{87}\right)\)
\(\chi_{4248}(71,\cdot)\) 4248.bs 58 no \(1\) \(1\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{25}{58}\right)\)
\(\chi_{4248}(73,\cdot)\) 4248.bj 58 no \(-1\) \(1\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{3}{58}\right)\)
\(\chi_{4248}(77,\cdot)\) 4248.ck 174 yes \(1\) \(1\) \(e\left(\frac{10}{87}\right)\) \(e\left(\frac{59}{87}\right)\) \(e\left(\frac{151}{174}\right)\) \(e\left(\frac{46}{87}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{25}{87}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{8}{87}\right)\) \(e\left(\frac{173}{174}\right)\)
\(\chi_{4248}(79,\cdot)\) 4248.cg 174 no \(-1\) \(1\) \(e\left(\frac{14}{87}\right)\) \(e\left(\frac{113}{174}\right)\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{47}{87}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{157}{174}\right)\) \(e\left(\frac{28}{87}\right)\) \(e\left(\frac{46}{87}\right)\) \(e\left(\frac{103}{174}\right)\)
\(\chi_{4248}(83,\cdot)\) 4248.ci 174 yes \(-1\) \(1\) \(e\left(\frac{71}{87}\right)\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{1}{87}\right)\) \(e\left(\frac{83}{87}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{7}{174}\right)\) \(e\left(\frac{55}{87}\right)\) \(e\left(\frac{22}{87}\right)\) \(e\left(\frac{53}{87}\right)\)
\(\chi_{4248}(85,\cdot)\) 4248.cb 174 yes \(1\) \(1\) \(e\left(\frac{161}{174}\right)\) \(e\left(\frac{53}{87}\right)\) \(e\left(\frac{115}{174}\right)\) \(e\left(\frac{149}{174}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{49}{87}\right)\) \(e\left(\frac{74}{87}\right)\) \(e\left(\frac{7}{174}\right)\) \(e\left(\frac{46}{87}\right)\)
\(\chi_{4248}(89,\cdot)\) 4248.bp 58 no \(1\) \(1\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{9}{58}\right)\)
\(\chi_{4248}(91,\cdot)\) 4248.bu 58 no \(1\) \(1\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{21}{29}\right)\)
\(\chi_{4248}(95,\cdot)\) 4248.ca 174 no \(1\) \(1\) \(e\left(\frac{125}{174}\right)\) \(e\left(\frac{85}{174}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{70}{87}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{4}{87}\right)\) \(e\left(\frac{38}{87}\right)\) \(e\left(\frac{13}{174}\right)\) \(e\left(\frac{59}{174}\right)\)
\(\chi_{4248}(97,\cdot)\) 4248.cj 174 no \(-1\) \(1\) \(e\left(\frac{32}{87}\right)\) \(e\left(\frac{67}{87}\right)\) \(e\left(\frac{83}{174}\right)\) \(e\left(\frac{103}{174}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{73}{174}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{43}{87}\right)\) \(e\left(\frac{49}{174}\right)\)
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