Properties

Modulus $1081$
Structure \(C_{506}\times C_{2}\)
Order $1012$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1081)
 
pari: g = idealstar(,1081,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1012
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{506}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1081}(189,\cdot)$, $\chi_{1081}(898,\cdot)$

First 32 of 1012 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{1081}(1,\cdot)\) 1081.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1081}(2,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{57}{253}\right)\) \(e\left(\frac{71}{253}\right)\) \(e\left(\frac{114}{253}\right)\) \(e\left(\frac{122}{253}\right)\) \(e\left(\frac{128}{253}\right)\) \(e\left(\frac{63}{253}\right)\) \(e\left(\frac{171}{253}\right)\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{179}{253}\right)\) \(e\left(\frac{141}{253}\right)\)
\(\chi_{1081}(3,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{71}{253}\right)\) \(e\left(\frac{84}{253}\right)\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{41}{253}\right)\) \(e\left(\frac{155}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{168}{253}\right)\) \(e\left(\frac{112}{253}\right)\) \(e\left(\frac{149}{253}\right)\)
\(\chi_{1081}(4,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{114}{253}\right)\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{228}{253}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{126}{253}\right)\) \(e\left(\frac{89}{253}\right)\) \(e\left(\frac{31}{253}\right)\) \(e\left(\frac{105}{253}\right)\) \(e\left(\frac{29}{253}\right)\)
\(\chi_{1081}(5,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{122}{253}\right)\) \(e\left(\frac{41}{253}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{17}{253}\right)\) \(e\left(\frac{163}{253}\right)\) \(e\left(\frac{283}{506}\right)\) \(e\left(\frac{113}{253}\right)\) \(e\left(\frac{82}{253}\right)\) \(e\left(\frac{139}{253}\right)\) \(e\left(\frac{142}{253}\right)\)
\(\chi_{1081}(6,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{128}{253}\right)\) \(e\left(\frac{155}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{163}{253}\right)\) \(e\left(\frac{30}{253}\right)\) \(e\left(\frac{248}{253}\right)\) \(e\left(\frac{131}{253}\right)\) \(e\left(\frac{57}{253}\right)\) \(e\left(\frac{38}{253}\right)\) \(e\left(\frac{37}{253}\right)\)
\(\chi_{1081}(7,\cdot)\) 1081.n 506 yes \(-1\) \(1\) \(e\left(\frac{63}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{126}{253}\right)\) \(e\left(\frac{283}{506}\right)\) \(e\left(\frac{248}{253}\right)\) \(e\left(\frac{339}{506}\right)\) \(e\left(\frac{189}{253}\right)\) \(e\left(\frac{117}{253}\right)\) \(e\left(\frac{409}{506}\right)\) \(e\left(\frac{325}{506}\right)\)
\(\chi_{1081}(8,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{171}{253}\right)\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{89}{253}\right)\) \(e\left(\frac{113}{253}\right)\) \(e\left(\frac{131}{253}\right)\) \(e\left(\frac{189}{253}\right)\) \(e\left(\frac{7}{253}\right)\) \(e\left(\frac{173}{253}\right)\) \(e\left(\frac{31}{253}\right)\) \(e\left(\frac{170}{253}\right)\)
\(\chi_{1081}(9,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{168}{253}\right)\) \(e\left(\frac{31}{253}\right)\) \(e\left(\frac{82}{253}\right)\) \(e\left(\frac{57}{253}\right)\) \(e\left(\frac{117}{253}\right)\) \(e\left(\frac{173}{253}\right)\) \(e\left(\frac{83}{253}\right)\) \(e\left(\frac{224}{253}\right)\) \(e\left(\frac{45}{253}\right)\)
\(\chi_{1081}(10,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{179}{253}\right)\) \(e\left(\frac{112}{253}\right)\) \(e\left(\frac{105}{253}\right)\) \(e\left(\frac{139}{253}\right)\) \(e\left(\frac{38}{253}\right)\) \(e\left(\frac{409}{506}\right)\) \(e\left(\frac{31}{253}\right)\) \(e\left(\frac{224}{253}\right)\) \(e\left(\frac{65}{253}\right)\) \(e\left(\frac{30}{253}\right)\)
\(\chi_{1081}(11,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{141}{253}\right)\) \(e\left(\frac{149}{253}\right)\) \(e\left(\frac{29}{253}\right)\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{37}{253}\right)\) \(e\left(\frac{325}{506}\right)\) \(e\left(\frac{170}{253}\right)\) \(e\left(\frac{45}{253}\right)\) \(e\left(\frac{30}{253}\right)\) \(e\left(\frac{189}{253}\right)\)
\(\chi_{1081}(12,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{226}{253}\right)\) \(e\left(\frac{117}{253}\right)\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{158}{253}\right)\) \(e\left(\frac{58}{253}\right)\) \(e\left(\frac{49}{253}\right)\) \(e\left(\frac{199}{253}\right)\) \(e\left(\frac{217}{253}\right)\) \(e\left(\frac{178}{253}\right)\)
\(\chi_{1081}(13,\cdot)\) 1081.o 506 yes \(-1\) \(1\) \(e\left(\frac{146}{253}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{39}{253}\right)\) \(e\left(\frac{443}{506}\right)\) \(e\left(\frac{137}{253}\right)\) \(e\left(\frac{188}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{235}{253}\right)\) \(e\left(\frac{229}{506}\right)\) \(e\left(\frac{203}{506}\right)\)
\(\chi_{1081}(14,\cdot)\) 1081.n 506 yes \(-1\) \(1\) \(e\left(\frac{120}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{240}{253}\right)\) \(e\left(\frac{21}{506}\right)\) \(e\left(\frac{123}{253}\right)\) \(e\left(\frac{465}{506}\right)\) \(e\left(\frac{107}{253}\right)\) \(e\left(\frac{6}{253}\right)\) \(e\left(\frac{261}{506}\right)\) \(e\left(\frac{101}{506}\right)\)
\(\chi_{1081}(15,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{193}{253}\right)\) \(e\left(\frac{125}{253}\right)\) \(e\left(\frac{133}{253}\right)\) \(e\left(\frac{58}{253}\right)\) \(e\left(\frac{65}{253}\right)\) \(e\left(\frac{147}{506}\right)\) \(e\left(\frac{73}{253}\right)\) \(e\left(\frac{250}{253}\right)\) \(e\left(\frac{251}{253}\right)\) \(e\left(\frac{38}{253}\right)\)
\(\chi_{1081}(16,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{228}{253}\right)\) \(e\left(\frac{31}{253}\right)\) \(e\left(\frac{203}{253}\right)\) \(e\left(\frac{235}{253}\right)\) \(e\left(\frac{6}{253}\right)\) \(e\left(\frac{252}{253}\right)\) \(e\left(\frac{178}{253}\right)\) \(e\left(\frac{62}{253}\right)\) \(e\left(\frac{210}{253}\right)\) \(e\left(\frac{58}{253}\right)\)
\(\chi_{1081}(17,\cdot)\) 1081.n 506 yes \(-1\) \(1\) \(e\left(\frac{227}{253}\right)\) \(e\left(\frac{12}{253}\right)\) \(e\left(\frac{201}{253}\right)\) \(e\left(\frac{337}{506}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{89}{506}\right)\) \(e\left(\frac{175}{253}\right)\) \(e\left(\frac{24}{253}\right)\) \(e\left(\frac{285}{506}\right)\) \(e\left(\frac{151}{506}\right)\)
\(\chi_{1081}(18,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{199}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{145}{253}\right)\) \(e\left(\frac{204}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{180}{253}\right)\) \(e\left(\frac{91}{253}\right)\) \(e\left(\frac{225}{253}\right)\) \(e\left(\frac{150}{253}\right)\) \(e\left(\frac{186}{253}\right)\)
\(\chi_{1081}(19,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{246}{253}\right)\) \(e\left(\frac{120}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{167}{253}\right)\) \(e\left(\frac{113}{253}\right)\) \(e\left(\frac{131}{506}\right)\) \(e\left(\frac{232}{253}\right)\) \(e\left(\frac{240}{253}\right)\) \(e\left(\frac{160}{253}\right)\) \(e\left(\frac{249}{253}\right)\)
\(\chi_{1081}(20,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{236}{253}\right)\) \(e\left(\frac{183}{253}\right)\) \(e\left(\frac{219}{253}\right)\) \(e\left(\frac{8}{253}\right)\) \(e\left(\frac{166}{253}\right)\) \(e\left(\frac{29}{506}\right)\) \(e\left(\frac{202}{253}\right)\) \(e\left(\frac{113}{253}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{171}{253}\right)\)
\(\chi_{1081}(21,\cdot)\) 1081.n 506 yes \(-1\) \(1\) \(e\left(\frac{134}{253}\right)\) \(e\left(\frac{16}{253}\right)\) \(e\left(\frac{15}{253}\right)\) \(e\left(\frac{365}{506}\right)\) \(e\left(\frac{150}{253}\right)\) \(e\left(\frac{203}{506}\right)\) \(e\left(\frac{149}{253}\right)\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{127}{506}\right)\) \(e\left(\frac{117}{506}\right)\)
\(\chi_{1081}(22,\cdot)\) 1081.j 46 yes \(1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{1081}(24,\cdot)\) 1081.i 23 no \(1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{1081}(25,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{82}{253}\right)\) \(e\left(\frac{235}{253}\right)\) \(e\left(\frac{34}{253}\right)\) \(e\left(\frac{73}{253}\right)\) \(e\left(\frac{30}{253}\right)\) \(e\left(\frac{226}{253}\right)\) \(e\left(\frac{164}{253}\right)\) \(e\left(\frac{25}{253}\right)\) \(e\left(\frac{31}{253}\right)\)
\(\chi_{1081}(26,\cdot)\) 1081.o 506 yes \(-1\) \(1\) \(e\left(\frac{203}{253}\right)\) \(e\left(\frac{62}{253}\right)\) \(e\left(\frac{153}{253}\right)\) \(e\left(\frac{181}{506}\right)\) \(e\left(\frac{12}{253}\right)\) \(e\left(\frac{251}{253}\right)\) \(e\left(\frac{103}{253}\right)\) \(e\left(\frac{124}{253}\right)\) \(e\left(\frac{81}{506}\right)\) \(e\left(\frac{485}{506}\right)\)
\(\chi_{1081}(27,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{252}{253}\right)\) \(e\left(\frac{173}{253}\right)\) \(e\left(\frac{123}{253}\right)\) \(e\left(\frac{212}{253}\right)\) \(e\left(\frac{49}{253}\right)\) \(e\left(\frac{133}{253}\right)\) \(e\left(\frac{251}{253}\right)\) \(e\left(\frac{83}{253}\right)\) \(e\left(\frac{194}{253}\right)\)
\(\chi_{1081}(28,\cdot)\) 1081.n 506 yes \(-1\) \(1\) \(e\left(\frac{177}{253}\right)\) \(e\left(\frac{74}{253}\right)\) \(e\left(\frac{101}{253}\right)\) \(e\left(\frac{265}{506}\right)\) \(e\left(\frac{251}{253}\right)\) \(e\left(\frac{85}{506}\right)\) \(e\left(\frac{25}{253}\right)\) \(e\left(\frac{148}{253}\right)\) \(e\left(\frac{113}{506}\right)\) \(e\left(\frac{383}{506}\right)\)
\(\chi_{1081}(29,\cdot)\) 1081.o 506 yes \(-1\) \(1\) \(e\left(\frac{84}{253}\right)\) \(e\left(\frac{78}{253}\right)\) \(e\left(\frac{168}{253}\right)\) \(e\left(\frac{293}{506}\right)\) \(e\left(\frac{162}{253}\right)\) \(e\left(\frac{226}{253}\right)\) \(e\left(\frac{252}{253}\right)\) \(e\left(\frac{156}{253}\right)\) \(e\left(\frac{461}{506}\right)\) \(e\left(\frac{349}{506}\right)\)
\(\chi_{1081}(30,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{250}{253}\right)\) \(e\left(\frac{196}{253}\right)\) \(e\left(\frac{247}{253}\right)\) \(e\left(\frac{180}{253}\right)\) \(e\left(\frac{193}{253}\right)\) \(e\left(\frac{273}{506}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{139}{253}\right)\) \(e\left(\frac{177}{253}\right)\) \(e\left(\frac{179}{253}\right)\)
\(\chi_{1081}(31,\cdot)\) 1081.o 506 yes \(-1\) \(1\) \(e\left(\frac{182}{253}\right)\) \(e\left(\frac{169}{253}\right)\) \(e\left(\frac{111}{253}\right)\) \(e\left(\frac{171}{506}\right)\) \(e\left(\frac{98}{253}\right)\) \(e\left(\frac{68}{253}\right)\) \(e\left(\frac{40}{253}\right)\) \(e\left(\frac{85}{253}\right)\) \(e\left(\frac{29}{506}\right)\) \(e\left(\frac{461}{506}\right)\)
\(\chi_{1081}(32,\cdot)\) 1081.m 253 yes \(1\) \(1\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{102}{253}\right)\) \(e\left(\frac{64}{253}\right)\) \(e\left(\frac{104}{253}\right)\) \(e\left(\frac{134}{253}\right)\) \(e\left(\frac{62}{253}\right)\) \(e\left(\frac{96}{253}\right)\) \(e\left(\frac{204}{253}\right)\) \(e\left(\frac{136}{253}\right)\) \(e\left(\frac{199}{253}\right)\)
\(\chi_{1081}(33,\cdot)\) 1081.p 506 yes \(1\) \(1\) \(e\left(\frac{212}{253}\right)\) \(e\left(\frac{233}{253}\right)\) \(e\left(\frac{171}{253}\right)\) \(e\left(\frac{183}{253}\right)\) \(e\left(\frac{192}{253}\right)\) \(e\left(\frac{189}{506}\right)\) \(e\left(\frac{130}{253}\right)\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{142}{253}\right)\) \(e\left(\frac{85}{253}\right)\)