Properties

Modulus $1441$
Structure \(C_{10}\times C_{130}\)
Order $1300$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1441)
 
pari: g = idealstar(,1441,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1300
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{10}\times C_{130}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1441}(1311,\cdot)$, $\chi_{1441}(133,\cdot)$

First 32 of 1300 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{1441}(1,\cdot)\) 1441.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1441}(2,\cdot)\) 1441.by 130 yes \(1\) \(1\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{37}{65}\right)\)
\(\chi_{1441}(3,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{64}{65}\right)\)
\(\chi_{1441}(4,\cdot)\) 1441.bi 65 yes \(1\) \(1\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{9}{65}\right)\)
\(\chi_{1441}(5,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{12}{65}\right)\)
\(\chi_{1441}(6,\cdot)\) 1441.bm 130 yes \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{36}{65}\right)\)
\(\chi_{1441}(7,\cdot)\) 1441.bn 130 yes \(-1\) \(1\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{103}{130}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{42}{65}\right)\)
\(\chi_{1441}(8,\cdot)\) 1441.by 130 yes \(1\) \(1\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{46}{65}\right)\)
\(\chi_{1441}(9,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{63}{65}\right)\)
\(\chi_{1441}(10,\cdot)\) 1441.ca 130 yes \(1\) \(1\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{49}{65}\right)\)
\(\chi_{1441}(12,\cdot)\) 1441.bl 65 no \(1\) \(1\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{8}{65}\right)\)
\(\chi_{1441}(13,\cdot)\) 1441.bn 130 yes \(-1\) \(1\) \(e\left(\frac{31}{130}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{93}{130}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{16}{65}\right)\)
\(\chi_{1441}(14,\cdot)\) 1441.bp 130 yes \(-1\) \(1\) \(e\left(\frac{71}{130}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{83}{130}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{9}{130}\right)\) \(e\left(\frac{14}{65}\right)\)
\(\chi_{1441}(15,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{11}{65}\right)\)
\(\chi_{1441}(16,\cdot)\) 1441.bi 65 yes \(1\) \(1\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{18}{65}\right)\)
\(\chi_{1441}(17,\cdot)\) 1441.bm 130 yes \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{7}{130}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{31}{65}\right)\)
\(\chi_{1441}(18,\cdot)\) 1441.bz 130 yes \(1\) \(1\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{1441}(19,\cdot)\) 1441.bz 130 yes \(1\) \(1\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{123}{130}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{1441}(20,\cdot)\) 1441.bh 65 yes \(1\) \(1\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{21}{65}\right)\)
\(\chi_{1441}(21,\cdot)\) 1441.bq 130 yes \(-1\) \(1\) \(e\left(\frac{103}{130}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{109}{130}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{49}{130}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{31}{130}\right)\) \(e\left(\frac{41}{65}\right)\)
\(\chi_{1441}(23,\cdot)\) 1441.bs 130 no \(-1\) \(1\) \(e\left(\frac{23}{130}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{69}{130}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{6}{65}\right)\)
\(\chi_{1441}(24,\cdot)\) 1441.bz 130 yes \(1\) \(1\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{1441}(25,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{24}{65}\right)\)
\(\chi_{1441}(26,\cdot)\) 1441.cd 130 yes \(-1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{53}{65}\right)\)
\(\chi_{1441}(27,\cdot)\) 1441.bj 65 yes \(1\) \(1\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{62}{65}\right)\)
\(\chi_{1441}(28,\cdot)\) 1441.cc 130 yes \(-1\) \(1\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{17}{130}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{121}{130}\right)\) \(e\left(\frac{51}{65}\right)\)
\(\chi_{1441}(29,\cdot)\) 1441.bx 130 yes \(1\) \(1\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{2}{65}\right)\)
\(\chi_{1441}(30,\cdot)\) 1441.bx 130 yes \(1\) \(1\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{48}{65}\right)\)
\(\chi_{1441}(31,\cdot)\) 1441.bp 130 yes \(-1\) \(1\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{89}{130}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{63}{130}\right)\) \(e\left(\frac{33}{65}\right)\)
\(\chi_{1441}(32,\cdot)\) 1441.bd 26 yes \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{1441}(34,\cdot)\) 1441.bl 65 no \(1\) \(1\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{3}{65}\right)\)
\(\chi_{1441}(35,\cdot)\) 1441.cc 130 yes \(-1\) \(1\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{83}{130}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{109}{130}\right)\) \(e\left(\frac{54}{65}\right)\)
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