Properties

Modulus $2151$
Structure \(C_{714}\times C_{2}\)
Order $1428$

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2151)
 
pari: g = idealstar(,2151,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1428
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{714}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2151}(1202,\cdot)$, $\chi_{2151}(955,\cdot)$

First 32 of 1428 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{2151}(1,\cdot)\) 2151.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2151}(2,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{335}{714}\right)\) \(e\left(\frac{335}{357}\right)\) \(e\left(\frac{73}{714}\right)\) \(e\left(\frac{337}{357}\right)\) \(e\left(\frac{97}{238}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{197}{714}\right)\) \(e\left(\frac{92}{357}\right)\) \(e\left(\frac{295}{714}\right)\) \(e\left(\frac{313}{357}\right)\)
\(\chi_{2151}(4,\cdot)\) 2151.bc 357 yes \(1\) \(1\) \(e\left(\frac{335}{357}\right)\) \(e\left(\frac{313}{357}\right)\) \(e\left(\frac{73}{357}\right)\) \(e\left(\frac{317}{357}\right)\) \(e\left(\frac{97}{119}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{197}{357}\right)\) \(e\left(\frac{184}{357}\right)\) \(e\left(\frac{295}{357}\right)\) \(e\left(\frac{269}{357}\right)\)
\(\chi_{2151}(5,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{73}{714}\right)\) \(e\left(\frac{73}{357}\right)\) \(e\left(\frac{131}{714}\right)\) \(e\left(\frac{326}{357}\right)\) \(e\left(\frac{73}{238}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{109}{714}\right)\) \(e\left(\frac{214}{357}\right)\) \(e\left(\frac{11}{714}\right)\) \(e\left(\frac{146}{357}\right)\)
\(\chi_{2151}(7,\cdot)\) 2151.bd 714 yes \(-1\) \(1\) \(e\left(\frac{337}{357}\right)\) \(e\left(\frac{317}{357}\right)\) \(e\left(\frac{326}{357}\right)\) \(e\left(\frac{479}{714}\right)\) \(e\left(\frac{99}{119}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{244}{357}\right)\) \(e\left(\frac{367}{714}\right)\) \(e\left(\frac{439}{714}\right)\) \(e\left(\frac{277}{357}\right)\)
\(\chi_{2151}(8,\cdot)\) 2151.ba 238 no \(-1\) \(1\) \(e\left(\frac{97}{238}\right)\) \(e\left(\frac{97}{119}\right)\) \(e\left(\frac{73}{238}\right)\) \(e\left(\frac{99}{119}\right)\) \(e\left(\frac{53}{238}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{197}{238}\right)\) \(e\left(\frac{92}{119}\right)\) \(e\left(\frac{57}{238}\right)\) \(e\left(\frac{75}{119}\right)\)
\(\chi_{2151}(10,\cdot)\) 2151.i 7 no \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{2151}(11,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{197}{714}\right)\) \(e\left(\frac{197}{357}\right)\) \(e\left(\frac{109}{714}\right)\) \(e\left(\frac{244}{357}\right)\) \(e\left(\frac{197}{238}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{167}{714}\right)\) \(e\left(\frac{20}{357}\right)\) \(e\left(\frac{685}{714}\right)\) \(e\left(\frac{37}{357}\right)\)
\(\chi_{2151}(13,\cdot)\) 2151.bd 714 yes \(-1\) \(1\) \(e\left(\frac{92}{357}\right)\) \(e\left(\frac{184}{357}\right)\) \(e\left(\frac{214}{357}\right)\) \(e\left(\frac{367}{714}\right)\) \(e\left(\frac{92}{119}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{357}\right)\) \(e\left(\frac{311}{714}\right)\) \(e\left(\frac{551}{714}\right)\) \(e\left(\frac{11}{357}\right)\)
\(\chi_{2151}(14,\cdot)\) 2151.bf 714 yes \(1\) \(1\) \(e\left(\frac{295}{714}\right)\) \(e\left(\frac{295}{357}\right)\) \(e\left(\frac{11}{714}\right)\) \(e\left(\frac{439}{714}\right)\) \(e\left(\frac{57}{238}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{685}{714}\right)\) \(e\left(\frac{551}{714}\right)\) \(e\left(\frac{10}{357}\right)\) \(e\left(\frac{233}{357}\right)\)
\(\chi_{2151}(16,\cdot)\) 2151.bc 357 yes \(1\) \(1\) \(e\left(\frac{313}{357}\right)\) \(e\left(\frac{269}{357}\right)\) \(e\left(\frac{146}{357}\right)\) \(e\left(\frac{277}{357}\right)\) \(e\left(\frac{75}{119}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{37}{357}\right)\) \(e\left(\frac{11}{357}\right)\) \(e\left(\frac{233}{357}\right)\) \(e\left(\frac{181}{357}\right)\)
\(\chi_{2151}(17,\cdot)\) 2151.ba 238 no \(-1\) \(1\) \(e\left(\frac{219}{238}\right)\) \(e\left(\frac{100}{119}\right)\) \(e\left(\frac{155}{238}\right)\) \(e\left(\frac{26}{119}\right)\) \(e\left(\frac{181}{238}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{89}{238}\right)\) \(e\left(\frac{47}{119}\right)\) \(e\left(\frac{33}{238}\right)\) \(e\left(\frac{81}{119}\right)\)
\(\chi_{2151}(19,\cdot)\) 2151.bb 238 no \(-1\) \(1\) \(e\left(\frac{117}{119}\right)\) \(e\left(\frac{115}{119}\right)\) \(e\left(\frac{104}{119}\right)\) \(e\left(\frac{155}{238}\right)\) \(e\left(\frac{113}{119}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{72}{119}\right)\) \(e\left(\frac{1}{238}\right)\) \(e\left(\frac{151}{238}\right)\) \(e\left(\frac{111}{119}\right)\)
\(\chi_{2151}(20,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{29}{714}\right)\) \(e\left(\frac{29}{357}\right)\) \(e\left(\frac{277}{714}\right)\) \(e\left(\frac{286}{357}\right)\) \(e\left(\frac{29}{238}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{503}{714}\right)\) \(e\left(\frac{41}{357}\right)\) \(e\left(\frac{601}{714}\right)\) \(e\left(\frac{58}{357}\right)\)
\(\chi_{2151}(22,\cdot)\) 2151.u 51 yes \(1\) \(1\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{50}{51}\right)\)
\(\chi_{2151}(23,\cdot)\) 2151.v 102 yes \(1\) \(1\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{31}{34}\right)\) \(1\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{11}{51}\right)\)
\(\chi_{2151}(25,\cdot)\) 2151.bc 357 yes \(1\) \(1\) \(e\left(\frac{73}{357}\right)\) \(e\left(\frac{146}{357}\right)\) \(e\left(\frac{131}{357}\right)\) \(e\left(\frac{295}{357}\right)\) \(e\left(\frac{73}{119}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{109}{357}\right)\) \(e\left(\frac{71}{357}\right)\) \(e\left(\frac{11}{357}\right)\) \(e\left(\frac{292}{357}\right)\)
\(\chi_{2151}(26,\cdot)\) 2151.z 238 no \(1\) \(1\) \(e\left(\frac{173}{238}\right)\) \(e\left(\frac{54}{119}\right)\) \(e\left(\frac{167}{238}\right)\) \(e\left(\frac{109}{238}\right)\) \(e\left(\frac{43}{238}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{79}{238}\right)\) \(e\left(\frac{165}{238}\right)\) \(e\left(\frac{22}{119}\right)\) \(e\left(\frac{108}{119}\right)\)
\(\chi_{2151}(28,\cdot)\) 2151.o 34 no \(-1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{2151}(29,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{383}{714}\right)\) \(e\left(\frac{26}{357}\right)\) \(e\left(\frac{433}{714}\right)\) \(e\left(\frac{121}{357}\right)\) \(e\left(\frac{145}{238}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{611}{714}\right)\) \(e\left(\frac{86}{357}\right)\) \(e\left(\frac{625}{714}\right)\) \(e\left(\frac{52}{357}\right)\)
\(\chi_{2151}(31,\cdot)\) 2151.bc 357 yes \(1\) \(1\) \(e\left(\frac{167}{357}\right)\) \(e\left(\frac{334}{357}\right)\) \(e\left(\frac{241}{357}\right)\) \(e\left(\frac{44}{357}\right)\) \(e\left(\frac{48}{119}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{176}{357}\right)\) \(e\left(\frac{226}{357}\right)\) \(e\left(\frac{211}{357}\right)\) \(e\left(\frac{311}{357}\right)\)
\(\chi_{2151}(32,\cdot)\) 2151.be 714 yes \(-1\) \(1\) \(e\left(\frac{247}{714}\right)\) \(e\left(\frac{247}{357}\right)\) \(e\left(\frac{365}{714}\right)\) \(e\left(\frac{257}{357}\right)\) \(e\left(\frac{9}{238}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{271}{714}\right)\) \(e\left(\frac{103}{357}\right)\) \(e\left(\frac{47}{714}\right)\) \(e\left(\frac{137}{357}\right)\)
\(\chi_{2151}(34,\cdot)\) 2151.bc 357 yes \(1\) \(1\) \(e\left(\frac{139}{357}\right)\) \(e\left(\frac{278}{357}\right)\) \(e\left(\frac{269}{357}\right)\) \(e\left(\frac{58}{357}\right)\) \(e\left(\frac{20}{119}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{232}{357}\right)\) \(e\left(\frac{233}{357}\right)\) \(e\left(\frac{197}{357}\right)\) \(e\left(\frac{199}{357}\right)\)
\(\chi_{2151}(35,\cdot)\) 2151.z 238 no \(1\) \(1\) \(e\left(\frac{11}{238}\right)\) \(e\left(\frac{11}{119}\right)\) \(e\left(\frac{23}{238}\right)\) \(e\left(\frac{139}{238}\right)\) \(e\left(\frac{33}{238}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{199}{238}\right)\) \(e\left(\frac{27}{238}\right)\) \(e\left(\frac{75}{119}\right)\) \(e\left(\frac{22}{119}\right)\)
\(\chi_{2151}(37,\cdot)\) 2151.bb 238 no \(-1\) \(1\) \(e\left(\frac{71}{119}\right)\) \(e\left(\frac{23}{119}\right)\) \(e\left(\frac{116}{119}\right)\) \(e\left(\frac{31}{238}\right)\) \(e\left(\frac{94}{119}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{62}{119}\right)\) \(e\left(\frac{143}{238}\right)\) \(e\left(\frac{173}{238}\right)\) \(e\left(\frac{46}{119}\right)\)
\(\chi_{2151}(38,\cdot)\) 2151.r 42 yes \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{2151}(40,\cdot)\) 2151.u 51 yes \(1\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(1\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{2}{51}\right)\)
\(\chi_{2151}(41,\cdot)\) 2151.bf 714 yes \(1\) \(1\) \(e\left(\frac{205}{714}\right)\) \(e\left(\frac{205}{357}\right)\) \(e\left(\frac{407}{714}\right)\) \(e\left(\frac{535}{714}\right)\) \(e\left(\frac{205}{238}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{355}{714}\right)\) \(e\left(\frac{395}{714}\right)\) \(e\left(\frac{13}{357}\right)\) \(e\left(\frac{53}{357}\right)\)
\(\chi_{2151}(43,\cdot)\) 2151.bd 714 yes \(-1\) \(1\) \(e\left(\frac{295}{357}\right)\) \(e\left(\frac{233}{357}\right)\) \(e\left(\frac{11}{357}\right)\) \(e\left(\frac{521}{714}\right)\) \(e\left(\frac{57}{119}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{328}{357}\right)\) \(e\left(\frac{31}{714}\right)\) \(e\left(\frac{397}{714}\right)\) \(e\left(\frac{109}{357}\right)\)
\(\chi_{2151}(44,\cdot)\) 2151.k 14 no \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{2151}(46,\cdot)\) 2151.bb 238 no \(-1\) \(1\) \(e\left(\frac{92}{119}\right)\) \(e\left(\frac{65}{119}\right)\) \(e\left(\frac{95}{119}\right)\) \(e\left(\frac{129}{238}\right)\) \(e\left(\frac{38}{119}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{20}{119}\right)\) \(e\left(\frac{73}{238}\right)\) \(e\left(\frac{75}{238}\right)\) \(e\left(\frac{11}{119}\right)\)
\(\chi_{2151}(47,\cdot)\) 2151.bf 714 yes \(1\) \(1\) \(e\left(\frac{359}{714}\right)\) \(e\left(\frac{2}{357}\right)\) \(e\left(\frac{253}{714}\right)\) \(e\left(\frac{101}{714}\right)\) \(e\left(\frac{121}{238}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{47}{714}\right)\) \(e\left(\frac{535}{714}\right)\) \(e\left(\frac{230}{357}\right)\) \(e\left(\frac{4}{357}\right)\)