Properties

Modulus 6011
Structure \(C_{6010}\)
Order 6010

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6011)
 
pari: g = idealstar(,6011,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 6010
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{6010}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6011}(2,\cdot)$

First 32 of 6010 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
\(\chi_{6011}(1,\cdot)\) 6011.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6011}(2,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{1}{6010}\right)\) \(e\left(\frac{447}{601}\right)\) \(e\left(\frac{1}{3005}\right)\) \(e\left(\frac{424}{3005}\right)\) \(e\left(\frac{4471}{6010}\right)\) \(e\left(\frac{1068}{3005}\right)\) \(e\left(\frac{3}{6010}\right)\) \(e\left(\frac{293}{601}\right)\) \(e\left(\frac{849}{6010}\right)\) \(e\left(\frac{4013}{6010}\right)\)
\(\chi_{6011}(3,\cdot)\) 6011.e 601 yes \(1\) \(1\) \(e\left(\frac{447}{601}\right)\) \(e\left(\frac{366}{601}\right)\) \(e\left(\frac{293}{601}\right)\) \(e\left(\frac{426}{601}\right)\) \(e\left(\frac{212}{601}\right)\) \(e\left(\frac{404}{601}\right)\) \(e\left(\frac{139}{601}\right)\) \(e\left(\frac{131}{601}\right)\) \(e\left(\frac{272}{601}\right)\) \(e\left(\frac{427}{601}\right)\)
\(\chi_{6011}(4,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{1}{3005}\right)\) \(e\left(\frac{293}{601}\right)\) \(e\left(\frac{2}{3005}\right)\) \(e\left(\frac{848}{3005}\right)\) \(e\left(\frac{1466}{3005}\right)\) \(e\left(\frac{2136}{3005}\right)\) \(e\left(\frac{3}{3005}\right)\) \(e\left(\frac{586}{601}\right)\) \(e\left(\frac{849}{3005}\right)\) \(e\left(\frac{1008}{3005}\right)\)
\(\chi_{6011}(5,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{424}{3005}\right)\) \(e\left(\frac{426}{601}\right)\) \(e\left(\frac{848}{3005}\right)\) \(e\left(\frac{1957}{3005}\right)\) \(e\left(\frac{2554}{3005}\right)\) \(e\left(\frac{1159}{3005}\right)\) \(e\left(\frac{1272}{3005}\right)\) \(e\left(\frac{251}{601}\right)\) \(e\left(\frac{2381}{3005}\right)\) \(e\left(\frac{682}{3005}\right)\)
\(\chi_{6011}(6,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{4471}{6010}\right)\) \(e\left(\frac{212}{601}\right)\) \(e\left(\frac{1466}{3005}\right)\) \(e\left(\frac{2554}{3005}\right)\) \(e\left(\frac{581}{6010}\right)\) \(e\left(\frac{83}{3005}\right)\) \(e\left(\frac{1393}{6010}\right)\) \(e\left(\frac{424}{601}\right)\) \(e\left(\frac{3569}{6010}\right)\) \(e\left(\frac{2273}{6010}\right)\)
\(\chi_{6011}(7,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{1068}{3005}\right)\) \(e\left(\frac{404}{601}\right)\) \(e\left(\frac{2136}{3005}\right)\) \(e\left(\frac{1159}{3005}\right)\) \(e\left(\frac{83}{3005}\right)\) \(e\left(\frac{453}{3005}\right)\) \(e\left(\frac{199}{3005}\right)\) \(e\left(\frac{207}{601}\right)\) \(e\left(\frac{2227}{3005}\right)\) \(e\left(\frac{754}{3005}\right)\)
\(\chi_{6011}(8,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{3}{6010}\right)\) \(e\left(\frac{139}{601}\right)\) \(e\left(\frac{3}{3005}\right)\) \(e\left(\frac{1272}{3005}\right)\) \(e\left(\frac{1393}{6010}\right)\) \(e\left(\frac{199}{3005}\right)\) \(e\left(\frac{9}{6010}\right)\) \(e\left(\frac{278}{601}\right)\) \(e\left(\frac{2547}{6010}\right)\) \(e\left(\frac{19}{6010}\right)\)
\(\chi_{6011}(9,\cdot)\) 6011.e 601 yes \(1\) \(1\) \(e\left(\frac{293}{601}\right)\) \(e\left(\frac{131}{601}\right)\) \(e\left(\frac{586}{601}\right)\) \(e\left(\frac{251}{601}\right)\) \(e\left(\frac{424}{601}\right)\) \(e\left(\frac{207}{601}\right)\) \(e\left(\frac{278}{601}\right)\) \(e\left(\frac{262}{601}\right)\) \(e\left(\frac{544}{601}\right)\) \(e\left(\frac{253}{601}\right)\)
\(\chi_{6011}(10,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{849}{6010}\right)\) \(e\left(\frac{272}{601}\right)\) \(e\left(\frac{849}{3005}\right)\) \(e\left(\frac{2381}{3005}\right)\) \(e\left(\frac{3569}{6010}\right)\) \(e\left(\frac{2227}{3005}\right)\) \(e\left(\frac{2547}{6010}\right)\) \(e\left(\frac{544}{601}\right)\) \(e\left(\frac{5611}{6010}\right)\) \(e\left(\frac{5377}{6010}\right)\)
\(\chi_{6011}(11,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{4013}{6010}\right)\) \(e\left(\frac{427}{601}\right)\) \(e\left(\frac{1008}{3005}\right)\) \(e\left(\frac{682}{3005}\right)\) \(e\left(\frac{2273}{6010}\right)\) \(e\left(\frac{754}{3005}\right)\) \(e\left(\frac{19}{6010}\right)\) \(e\left(\frac{253}{601}\right)\) \(e\left(\frac{5377}{6010}\right)\) \(e\left(\frac{3379}{6010}\right)\)
\(\chi_{6011}(12,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{2236}{3005}\right)\) \(e\left(\frac{58}{601}\right)\) \(e\left(\frac{1467}{3005}\right)\) \(e\left(\frac{2978}{3005}\right)\) \(e\left(\frac{2526}{3005}\right)\) \(e\left(\frac{1151}{3005}\right)\) \(e\left(\frac{698}{3005}\right)\) \(e\left(\frac{116}{601}\right)\) \(e\left(\frac{2209}{3005}\right)\) \(e\left(\frac{138}{3005}\right)\)
\(\chi_{6011}(13,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{5253}{6010}\right)\) \(e\left(\frac{585}{601}\right)\) \(e\left(\frac{2248}{3005}\right)\) \(e\left(\frac{567}{3005}\right)\) \(e\left(\frac{5093}{6010}\right)\) \(e\left(\frac{2874}{3005}\right)\) \(e\left(\frac{3739}{6010}\right)\) \(e\left(\frac{569}{601}\right)\) \(e\left(\frac{377}{6010}\right)\) \(e\left(\frac{3219}{6010}\right)\)
\(\chi_{6011}(14,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{2137}{6010}\right)\) \(e\left(\frac{250}{601}\right)\) \(e\left(\frac{2137}{3005}\right)\) \(e\left(\frac{1583}{3005}\right)\) \(e\left(\frac{4637}{6010}\right)\) \(e\left(\frac{1521}{3005}\right)\) \(e\left(\frac{401}{6010}\right)\) \(e\left(\frac{500}{601}\right)\) \(e\left(\frac{5303}{6010}\right)\) \(e\left(\frac{5521}{6010}\right)\)
\(\chi_{6011}(15,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{2659}{3005}\right)\) \(e\left(\frac{191}{601}\right)\) \(e\left(\frac{2313}{3005}\right)\) \(e\left(\frac{1082}{3005}\right)\) \(e\left(\frac{609}{3005}\right)\) \(e\left(\frac{174}{3005}\right)\) \(e\left(\frac{1967}{3005}\right)\) \(e\left(\frac{382}{601}\right)\) \(e\left(\frac{736}{3005}\right)\) \(e\left(\frac{2817}{3005}\right)\)
\(\chi_{6011}(16,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{2}{3005}\right)\) \(e\left(\frac{586}{601}\right)\) \(e\left(\frac{4}{3005}\right)\) \(e\left(\frac{1696}{3005}\right)\) \(e\left(\frac{2932}{3005}\right)\) \(e\left(\frac{1267}{3005}\right)\) \(e\left(\frac{6}{3005}\right)\) \(e\left(\frac{571}{601}\right)\) \(e\left(\frac{1698}{3005}\right)\) \(e\left(\frac{2016}{3005}\right)\)
\(\chi_{6011}(17,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{377}{6010}\right)\) \(e\left(\frac{239}{601}\right)\) \(e\left(\frac{377}{3005}\right)\) \(e\left(\frac{583}{3005}\right)\) \(e\left(\frac{2767}{6010}\right)\) \(e\left(\frac{2971}{3005}\right)\) \(e\left(\frac{1131}{6010}\right)\) \(e\left(\frac{478}{601}\right)\) \(e\left(\frac{1543}{6010}\right)\) \(e\left(\frac{4391}{6010}\right)\)
\(\chi_{6011}(18,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{2931}{6010}\right)\) \(e\left(\frac{578}{601}\right)\) \(e\left(\frac{2931}{3005}\right)\) \(e\left(\frac{1679}{3005}\right)\) \(e\left(\frac{2701}{6010}\right)\) \(e\left(\frac{2103}{3005}\right)\) \(e\left(\frac{2783}{6010}\right)\) \(e\left(\frac{555}{601}\right)\) \(e\left(\frac{279}{6010}\right)\) \(e\left(\frac{533}{6010}\right)\)
\(\chi_{6011}(19,\cdot)\) 6011.f 1202 yes \(-1\) \(1\) \(e\left(\frac{469}{1202}\right)\) \(e\left(\frac{71}{601}\right)\) \(e\left(\frac{469}{601}\right)\) \(e\left(\frac{526}{601}\right)\) \(e\left(\frac{611}{1202}\right)\) \(e\left(\frac{259}{601}\right)\) \(e\left(\frac{205}{1202}\right)\) \(e\left(\frac{142}{601}\right)\) \(e\left(\frac{319}{1202}\right)\) \(e\left(\frac{967}{1202}\right)\)
\(\chi_{6011}(20,\cdot)\) 6011.e 601 yes \(1\) \(1\) \(e\left(\frac{85}{601}\right)\) \(e\left(\frac{118}{601}\right)\) \(e\left(\frac{170}{601}\right)\) \(e\left(\frac{561}{601}\right)\) \(e\left(\frac{203}{601}\right)\) \(e\left(\frac{58}{601}\right)\) \(e\left(\frac{255}{601}\right)\) \(e\left(\frac{236}{601}\right)\) \(e\left(\frac{45}{601}\right)\) \(e\left(\frac{338}{601}\right)\)
\(\chi_{6011}(21,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{298}{3005}\right)\) \(e\left(\frac{169}{601}\right)\) \(e\left(\frac{596}{3005}\right)\) \(e\left(\frac{284}{3005}\right)\) \(e\left(\frac{1143}{3005}\right)\) \(e\left(\frac{2473}{3005}\right)\) \(e\left(\frac{894}{3005}\right)\) \(e\left(\frac{338}{601}\right)\) \(e\left(\frac{582}{3005}\right)\) \(e\left(\frac{2889}{3005}\right)\)
\(\chi_{6011}(22,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{2007}{3005}\right)\) \(e\left(\frac{273}{601}\right)\) \(e\left(\frac{1009}{3005}\right)\) \(e\left(\frac{1106}{3005}\right)\) \(e\left(\frac{367}{3005}\right)\) \(e\left(\frac{1822}{3005}\right)\) \(e\left(\frac{11}{3005}\right)\) \(e\left(\frac{546}{601}\right)\) \(e\left(\frac{108}{3005}\right)\) \(e\left(\frac{691}{3005}\right)\)
\(\chi_{6011}(23,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{4739}{6010}\right)\) \(e\left(\frac{409}{601}\right)\) \(e\left(\frac{1734}{3005}\right)\) \(e\left(\frac{1996}{3005}\right)\) \(e\left(\frac{2819}{6010}\right)\) \(e\left(\frac{832}{3005}\right)\) \(e\left(\frac{2197}{6010}\right)\) \(e\left(\frac{217}{601}\right)\) \(e\left(\frac{2721}{6010}\right)\) \(e\left(\frac{1967}{6010}\right)\)
\(\chi_{6011}(24,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{4473}{6010}\right)\) \(e\left(\frac{505}{601}\right)\) \(e\left(\frac{1468}{3005}\right)\) \(e\left(\frac{397}{3005}\right)\) \(e\left(\frac{3513}{6010}\right)\) \(e\left(\frac{2219}{3005}\right)\) \(e\left(\frac{1399}{6010}\right)\) \(e\left(\frac{409}{601}\right)\) \(e\left(\frac{5267}{6010}\right)\) \(e\left(\frac{4289}{6010}\right)\)
\(\chi_{6011}(25,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{848}{3005}\right)\) \(e\left(\frac{251}{601}\right)\) \(e\left(\frac{1696}{3005}\right)\) \(e\left(\frac{909}{3005}\right)\) \(e\left(\frac{2103}{3005}\right)\) \(e\left(\frac{2318}{3005}\right)\) \(e\left(\frac{2544}{3005}\right)\) \(e\left(\frac{502}{601}\right)\) \(e\left(\frac{1757}{3005}\right)\) \(e\left(\frac{1364}{3005}\right)\)
\(\chi_{6011}(26,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{2627}{3005}\right)\) \(e\left(\frac{431}{601}\right)\) \(e\left(\frac{2249}{3005}\right)\) \(e\left(\frac{991}{3005}\right)\) \(e\left(\frac{1777}{3005}\right)\) \(e\left(\frac{937}{3005}\right)\) \(e\left(\frac{1871}{3005}\right)\) \(e\left(\frac{261}{601}\right)\) \(e\left(\frac{613}{3005}\right)\) \(e\left(\frac{611}{3005}\right)\)
\(\chi_{6011}(27,\cdot)\) 6011.e 601 yes \(1\) \(1\) \(e\left(\frac{139}{601}\right)\) \(e\left(\frac{497}{601}\right)\) \(e\left(\frac{278}{601}\right)\) \(e\left(\frac{76}{601}\right)\) \(e\left(\frac{35}{601}\right)\) \(e\left(\frac{10}{601}\right)\) \(e\left(\frac{417}{601}\right)\) \(e\left(\frac{393}{601}\right)\) \(e\left(\frac{215}{601}\right)\) \(e\left(\frac{79}{601}\right)\)
\(\chi_{6011}(28,\cdot)\) 6011.g 3005 yes \(1\) \(1\) \(e\left(\frac{1069}{3005}\right)\) \(e\left(\frac{96}{601}\right)\) \(e\left(\frac{2138}{3005}\right)\) \(e\left(\frac{2007}{3005}\right)\) \(e\left(\frac{1549}{3005}\right)\) \(e\left(\frac{2589}{3005}\right)\) \(e\left(\frac{202}{3005}\right)\) \(e\left(\frac{192}{601}\right)\) \(e\left(\frac{71}{3005}\right)\) \(e\left(\frac{1762}{3005}\right)\)
\(\chi_{6011}(29,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{1349}{6010}\right)\) \(e\left(\frac{200}{601}\right)\) \(e\left(\frac{1349}{3005}\right)\) \(e\left(\frac{1026}{3005}\right)\) \(e\left(\frac{3349}{6010}\right)\) \(e\left(\frac{1337}{3005}\right)\) \(e\left(\frac{4047}{6010}\right)\) \(e\left(\frac{400}{601}\right)\) \(e\left(\frac{3401}{6010}\right)\) \(e\left(\frac{4537}{6010}\right)\)
\(\chi_{6011}(30,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{5319}{6010}\right)\) \(e\left(\frac{37}{601}\right)\) \(e\left(\frac{2314}{3005}\right)\) \(e\left(\frac{1506}{3005}\right)\) \(e\left(\frac{5689}{6010}\right)\) \(e\left(\frac{1242}{3005}\right)\) \(e\left(\frac{3937}{6010}\right)\) \(e\left(\frac{74}{601}\right)\) \(e\left(\frac{2321}{6010}\right)\) \(e\left(\frac{3637}{6010}\right)\)
\(\chi_{6011}(31,\cdot)\) 6011.h 6010 yes \(-1\) \(1\) \(e\left(\frac{1827}{6010}\right)\) \(e\left(\frac{511}{601}\right)\) \(e\left(\frac{1827}{3005}\right)\) \(e\left(\frac{2363}{3005}\right)\) \(e\left(\frac{927}{6010}\right)\) \(e\left(\frac{991}{3005}\right)\) \(e\left(\frac{5481}{6010}\right)\) \(e\left(\frac{421}{601}\right)\) \(e\left(\frac{543}{6010}\right)\) \(e\left(\frac{5561}{6010}\right)\)
\(\chi_{6011}(32,\cdot)\) 6011.f 1202 yes \(-1\) \(1\) \(e\left(\frac{1}{1202}\right)\) \(e\left(\frac{432}{601}\right)\) \(e\left(\frac{1}{601}\right)\) \(e\left(\frac{424}{601}\right)\) \(e\left(\frac{865}{1202}\right)\) \(e\left(\frac{467}{601}\right)\) \(e\left(\frac{3}{1202}\right)\) \(e\left(\frac{263}{601}\right)\) \(e\left(\frac{849}{1202}\right)\) \(e\left(\frac{407}{1202}\right)\)