Properties

Modulus $1048$
Structure \(C_{130}\times C_{2}\times C_{2}\)
Order $520$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1048)
 
pari: g = idealstar(,1048,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 520
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{130}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1048}(263,\cdot)$, $\chi_{1048}(525,\cdot)$, $\chi_{1048}(657,\cdot)$

First 32 of 520 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{1048}(1,\cdot)\) 1048.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1048}(3,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{71}{130}\right)\)
\(\chi_{1048}(5,\cdot)\) 1048.ba 130 yes \(1\) \(1\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{101}{130}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{123}{130}\right)\)
\(\chi_{1048}(7,\cdot)\) 1048.bc 130 no \(-1\) \(1\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{83}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{4}{65}\right)\)
\(\chi_{1048}(9,\cdot)\) 1048.y 65 no \(1\) \(1\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{6}{65}\right)\)
\(\chi_{1048}(11,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{33}{130}\right)\) \(e\left(\frac{43}{130}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{113}{130}\right)\)
\(\chi_{1048}(13,\cdot)\) 1048.ba 130 yes \(1\) \(1\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{33}{130}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{99}{130}\right)\)
\(\chi_{1048}(15,\cdot)\) 1048.bc 130 no \(-1\) \(1\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{83}{130}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{43}{130}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{79}{130}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{32}{65}\right)\)
\(\chi_{1048}(17,\cdot)\) 1048.bf 130 no \(-1\) \(1\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{29}{130}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{37}{65}\right)\)
\(\chi_{1048}(19,\cdot)\) 1048.t 26 yes \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{1048}(21,\cdot)\) 1048.ba 130 yes \(1\) \(1\) \(e\left(\frac{71}{130}\right)\) \(e\left(\frac{123}{130}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{99}{130}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{79}{130}\right)\)
\(\chi_{1048}(23,\cdot)\) 1048.bb 130 no \(1\) \(1\) \(e\left(\frac{31}{130}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{63}{130}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{53}{130}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{49}{130}\right)\) \(e\left(\frac{79}{130}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{47}{65}\right)\)
\(\chi_{1048}(25,\cdot)\) 1048.y 65 no \(1\) \(1\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{58}{65}\right)\)
\(\chi_{1048}(27,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{121}{130}\right)\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{53}{130}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{83}{130}\right)\)
\(\chi_{1048}(29,\cdot)\) 1048.z 130 yes \(-1\) \(1\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{71}{130}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{53}{130}\right)\)
\(\chi_{1048}(31,\cdot)\) 1048.bb 130 no \(1\) \(1\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{77}{130}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{31}{65}\right)\)
\(\chi_{1048}(33,\cdot)\) 1048.y 65 no \(1\) \(1\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{27}{65}\right)\)
\(\chi_{1048}(35,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{47}{130}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{21}{130}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{130}\right)\)
\(\chi_{1048}(37,\cdot)\) 1048.z 130 yes \(-1\) \(1\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{21}{130}\right)\) \(e\left(\frac{23}{130}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{63}{130}\right)\)
\(\chi_{1048}(39,\cdot)\) 1048.u 26 no \(-1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{1048}(41,\cdot)\) 1048.y 65 no \(1\) \(1\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{54}{65}\right)\)
\(\chi_{1048}(43,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{49}{130}\right)\) \(e\left(\frac{9}{130}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{7}{130}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{97}{130}\right)\)
\(\chi_{1048}(45,\cdot)\) 1048.w 26 yes \(1\) \(1\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{1048}(47,\cdot)\) 1048.v 26 no \(1\) \(1\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{1048}(49,\cdot)\) 1048.y 65 no \(1\) \(1\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{8}{65}\right)\)
\(\chi_{1048}(51,\cdot)\) 1048.t 26 yes \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{1048}(53,\cdot)\) 1048.o 10 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1048}(55,\cdot)\) 1048.bc 130 no \(-1\) \(1\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{53}{65}\right)\)
\(\chi_{1048}(57,\cdot)\) 1048.bf 130 no \(-1\) \(1\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{18}{65}\right)\)
\(\chi_{1048}(59,\cdot)\) 1048.be 130 yes \(-1\) \(1\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{67}{130}\right)\) \(e\left(\frac{7}{130}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{121}{130}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{61}{130}\right)\)
\(\chi_{1048}(61,\cdot)\) 1048.o 10 yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1048}(63,\cdot)\) 1048.u 26 no \(-1\) \(1\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{2}{13}\right)\)