Properties

Modulus 4013
Structure \(C_{4012}\)
Order 4012

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4013)
pari: g = idealstar(,4013,2)

Character group

sage: G.order()
pari: g.no
Order = 4012
sage: H.invariants()
pari: g.cyc
Structure = \(C_{4012}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4013}(2,\cdot)$

First 32 of 4012 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
\(\chi_{4013}(1,\cdot)\) 4013.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4013}(2,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{1}{4012}\right)\) \(e\left(\frac{1745}{4012}\right)\) \(e\left(\frac{1}{2006}\right)\) \(e\left(\frac{2241}{4012}\right)\) \(e\left(\frac{873}{2006}\right)\) \(e\left(\frac{653}{1003}\right)\) \(e\left(\frac{3}{4012}\right)\) \(e\left(\frac{1745}{2006}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{543}{1003}\right)\)
\(\chi_{4013}(3,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{1745}{4012}\right)\) \(e\left(\frac{3929}{4012}\right)\) \(e\left(\frac{1745}{2006}\right)\) \(e\left(\frac{2857}{4012}\right)\) \(e\left(\frac{831}{2006}\right)\) \(e\left(\frac{77}{1003}\right)\) \(e\left(\frac{1223}{4012}\right)\) \(e\left(\frac{1923}{2006}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{703}{1003}\right)\)
\(\chi_{4013}(4,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1}{2006}\right)\) \(e\left(\frac{1745}{2006}\right)\) \(e\left(\frac{1}{1003}\right)\) \(e\left(\frac{235}{2006}\right)\) \(e\left(\frac{873}{1003}\right)\) \(e\left(\frac{303}{1003}\right)\) \(e\left(\frac{3}{2006}\right)\) \(e\left(\frac{742}{1003}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{83}{1003}\right)\)
\(\chi_{4013}(5,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{2241}{4012}\right)\) \(e\left(\frac{2857}{4012}\right)\) \(e\left(\frac{235}{2006}\right)\) \(e\left(\frac{3069}{4012}\right)\) \(e\left(\frac{543}{2006}\right)\) \(e\left(\frac{999}{1003}\right)\) \(e\left(\frac{2711}{4012}\right)\) \(e\left(\frac{851}{2006}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{224}{1003}\right)\)
\(\chi_{4013}(6,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{873}{2006}\right)\) \(e\left(\frac{831}{2006}\right)\) \(e\left(\frac{873}{1003}\right)\) \(e\left(\frac{543}{2006}\right)\) \(e\left(\frac{852}{1003}\right)\) \(e\left(\frac{730}{1003}\right)\) \(e\left(\frac{613}{2006}\right)\) \(e\left(\frac{831}{1003}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{243}{1003}\right)\)
\(\chi_{4013}(7,\cdot)\) 4013.j 1003 Yes \(1\) \(1\) \(e\left(\frac{653}{1003}\right)\) \(e\left(\frac{77}{1003}\right)\) \(e\left(\frac{303}{1003}\right)\) \(e\left(\frac{999}{1003}\right)\) \(e\left(\frac{730}{1003}\right)\) \(e\left(\frac{536}{1003}\right)\) \(e\left(\frac{956}{1003}\right)\) \(e\left(\frac{154}{1003}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{74}{1003}\right)\)
\(\chi_{4013}(8,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{3}{4012}\right)\) \(e\left(\frac{1223}{4012}\right)\) \(e\left(\frac{3}{2006}\right)\) \(e\left(\frac{2711}{4012}\right)\) \(e\left(\frac{613}{2006}\right)\) \(e\left(\frac{956}{1003}\right)\) \(e\left(\frac{9}{4012}\right)\) \(e\left(\frac{1223}{2006}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{626}{1003}\right)\)
\(\chi_{4013}(9,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1745}{2006}\right)\) \(e\left(\frac{1923}{2006}\right)\) \(e\left(\frac{742}{1003}\right)\) \(e\left(\frac{851}{2006}\right)\) \(e\left(\frac{831}{1003}\right)\) \(e\left(\frac{154}{1003}\right)\) \(e\left(\frac{1223}{2006}\right)\) \(e\left(\frac{920}{1003}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{403}{1003}\right)\)
\(\chi_{4013}(10,\cdot)\) 4013.e 34 Yes \(1\) \(1\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{4013}(11,\cdot)\) 4013.j 1003 Yes \(1\) \(1\) \(e\left(\frac{543}{1003}\right)\) \(e\left(\frac{703}{1003}\right)\) \(e\left(\frac{83}{1003}\right)\) \(e\left(\frac{224}{1003}\right)\) \(e\left(\frac{243}{1003}\right)\) \(e\left(\frac{74}{1003}\right)\) \(e\left(\frac{626}{1003}\right)\) \(e\left(\frac{403}{1003}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{871}{1003}\right)\)
\(\chi_{4013}(12,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{1747}{4012}\right)\) \(e\left(\frac{3407}{4012}\right)\) \(e\left(\frac{1747}{2006}\right)\) \(e\left(\frac{3327}{4012}\right)\) \(e\left(\frac{571}{2006}\right)\) \(e\left(\frac{380}{1003}\right)\) \(e\left(\frac{1229}{4012}\right)\) \(e\left(\frac{1401}{2006}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{786}{1003}\right)\)
\(\chi_{4013}(13,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{355}{2006}\right)\) \(e\left(\frac{1627}{2006}\right)\) \(e\left(\frac{355}{1003}\right)\) \(e\left(\frac{1179}{2006}\right)\) \(e\left(\frac{991}{1003}\right)\) \(e\left(\frac{244}{1003}\right)\) \(e\left(\frac{1065}{2006}\right)\) \(e\left(\frac{624}{1003}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{378}{1003}\right)\)
\(\chi_{4013}(14,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{2613}{4012}\right)\) \(e\left(\frac{2053}{4012}\right)\) \(e\left(\frac{607}{2006}\right)\) \(e\left(\frac{2225}{4012}\right)\) \(e\left(\frac{327}{2006}\right)\) \(e\left(\frac{186}{1003}\right)\) \(e\left(\frac{3827}{4012}\right)\) \(e\left(\frac{47}{2006}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{617}{1003}\right)\)
\(\chi_{4013}(15,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1993}{2006}\right)\) \(e\left(\frac{1387}{2006}\right)\) \(e\left(\frac{990}{1003}\right)\) \(e\left(\frac{957}{2006}\right)\) \(e\left(\frac{687}{1003}\right)\) \(e\left(\frac{73}{1003}\right)\) \(e\left(\frac{1967}{2006}\right)\) \(e\left(\frac{384}{1003}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{927}{1003}\right)\)
\(\chi_{4013}(16,\cdot)\) 4013.j 1003 Yes \(1\) \(1\) \(e\left(\frac{1}{1003}\right)\) \(e\left(\frac{742}{1003}\right)\) \(e\left(\frac{2}{1003}\right)\) \(e\left(\frac{235}{1003}\right)\) \(e\left(\frac{743}{1003}\right)\) \(e\left(\frac{606}{1003}\right)\) \(e\left(\frac{3}{1003}\right)\) \(e\left(\frac{481}{1003}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{166}{1003}\right)\)
\(\chi_{4013}(17,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1329}{2006}\right)\) \(e\left(\frac{169}{2006}\right)\) \(e\left(\frac{326}{1003}\right)\) \(e\left(\frac{1385}{2006}\right)\) \(e\left(\frac{749}{1003}\right)\) \(e\left(\frac{484}{1003}\right)\) \(e\left(\frac{1981}{2006}\right)\) \(e\left(\frac{169}{1003}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{980}{1003}\right)\)
\(\chi_{4013}(18,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{3491}{4012}\right)\) \(e\left(\frac{1579}{4012}\right)\) \(e\left(\frac{1485}{2006}\right)\) \(e\left(\frac{3943}{4012}\right)\) \(e\left(\frac{529}{2006}\right)\) \(e\left(\frac{807}{1003}\right)\) \(e\left(\frac{2449}{4012}\right)\) \(e\left(\frac{1579}{2006}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{946}{1003}\right)\)
\(\chi_{4013}(19,\cdot)\) 4013.j 1003 Yes \(1\) \(1\) \(e\left(\frac{524}{1003}\right)\) \(e\left(\frac{647}{1003}\right)\) \(e\left(\frac{45}{1003}\right)\) \(e\left(\frac{774}{1003}\right)\) \(e\left(\frac{168}{1003}\right)\) \(e\left(\frac{596}{1003}\right)\) \(e\left(\frac{569}{1003}\right)\) \(e\left(\frac{291}{1003}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{726}{1003}\right)\)
\(\chi_{4013}(20,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{2243}{4012}\right)\) \(e\left(\frac{2335}{4012}\right)\) \(e\left(\frac{237}{2006}\right)\) \(e\left(\frac{3539}{4012}\right)\) \(e\left(\frac{283}{2006}\right)\) \(e\left(\frac{299}{1003}\right)\) \(e\left(\frac{2717}{4012}\right)\) \(e\left(\frac{329}{2006}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{307}{1003}\right)\)
\(\chi_{4013}(21,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{345}{4012}\right)\) \(e\left(\frac{225}{4012}\right)\) \(e\left(\frac{345}{2006}\right)\) \(e\left(\frac{2841}{4012}\right)\) \(e\left(\frac{285}{2006}\right)\) \(e\left(\frac{613}{1003}\right)\) \(e\left(\frac{1035}{4012}\right)\) \(e\left(\frac{225}{2006}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{777}{1003}\right)\)
\(\chi_{4013}(22,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{2173}{4012}\right)\) \(e\left(\frac{545}{4012}\right)\) \(e\left(\frac{167}{2006}\right)\) \(e\left(\frac{3137}{4012}\right)\) \(e\left(\frac{1359}{2006}\right)\) \(e\left(\frac{727}{1003}\right)\) \(e\left(\frac{2507}{4012}\right)\) \(e\left(\frac{545}{2006}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{411}{1003}\right)\)
\(\chi_{4013}(23,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{2677}{4012}\right)\) \(e\left(\frac{1397}{4012}\right)\) \(e\left(\frac{671}{2006}\right)\) \(e\left(\frac{1217}{4012}\right)\) \(e\left(\frac{31}{2006}\right)\) \(e\left(\frac{855}{1003}\right)\) \(e\left(\frac{7}{4012}\right)\) \(e\left(\frac{1397}{2006}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{264}{1003}\right)\)
\(\chi_{4013}(24,\cdot)\) 4013.j 1003 Yes \(1\) \(1\) \(e\left(\frac{437}{1003}\right)\) \(e\left(\frac{285}{1003}\right)\) \(e\left(\frac{874}{1003}\right)\) \(e\left(\frac{389}{1003}\right)\) \(e\left(\frac{722}{1003}\right)\) \(e\left(\frac{30}{1003}\right)\) \(e\left(\frac{308}{1003}\right)\) \(e\left(\frac{570}{1003}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{326}{1003}\right)\)
\(\chi_{4013}(25,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{235}{2006}\right)\) \(e\left(\frac{851}{2006}\right)\) \(e\left(\frac{235}{1003}\right)\) \(e\left(\frac{1063}{2006}\right)\) \(e\left(\frac{543}{1003}\right)\) \(e\left(\frac{995}{1003}\right)\) \(e\left(\frac{705}{2006}\right)\) \(e\left(\frac{851}{1003}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{448}{1003}\right)\)
\(\chi_{4013}(26,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{711}{4012}\right)\) \(e\left(\frac{987}{4012}\right)\) \(e\left(\frac{711}{2006}\right)\) \(e\left(\frac{587}{4012}\right)\) \(e\left(\frac{849}{2006}\right)\) \(e\left(\frac{897}{1003}\right)\) \(e\left(\frac{2133}{4012}\right)\) \(e\left(\frac{987}{2006}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{921}{1003}\right)\)
\(\chi_{4013}(27,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{1223}{4012}\right)\) \(e\left(\frac{3763}{4012}\right)\) \(e\left(\frac{1223}{2006}\right)\) \(e\left(\frac{547}{4012}\right)\) \(e\left(\frac{487}{2006}\right)\) \(e\left(\frac{231}{1003}\right)\) \(e\left(\frac{3669}{4012}\right)\) \(e\left(\frac{1757}{2006}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{103}{1003}\right)\)
\(\chi_{4013}(28,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1307}{2006}\right)\) \(e\left(\frac{1899}{2006}\right)\) \(e\left(\frac{304}{1003}\right)\) \(e\left(\frac{227}{2006}\right)\) \(e\left(\frac{600}{1003}\right)\) \(e\left(\frac{839}{1003}\right)\) \(e\left(\frac{1915}{2006}\right)\) \(e\left(\frac{896}{1003}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{157}{1003}\right)\)
\(\chi_{4013}(29,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{3767}{4012}\right)\) \(e\left(\frac{1759}{4012}\right)\) \(e\left(\frac{1761}{2006}\right)\) \(e\left(\frac{599}{4012}\right)\) \(e\left(\frac{757}{2006}\right)\) \(e\left(\frac{495}{1003}\right)\) \(e\left(\frac{3277}{4012}\right)\) \(e\left(\frac{1759}{2006}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{364}{1003}\right)\)
\(\chi_{4013}(30,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{3987}{4012}\right)\) \(e\left(\frac{507}{4012}\right)\) \(e\left(\frac{1981}{2006}\right)\) \(e\left(\frac{143}{4012}\right)\) \(e\left(\frac{241}{2006}\right)\) \(e\left(\frac{726}{1003}\right)\) \(e\left(\frac{3937}{4012}\right)\) \(e\left(\frac{507}{2006}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{467}{1003}\right)\)
\(\chi_{4013}(31,\cdot)\) 4013.k 2006 Yes \(1\) \(1\) \(e\left(\frac{1859}{2006}\right)\) \(e\left(\frac{253}{2006}\right)\) \(e\left(\frac{856}{1003}\right)\) \(e\left(\frac{1563}{2006}\right)\) \(e\left(\frac{53}{1003}\right)\) \(e\left(\frac{594}{1003}\right)\) \(e\left(\frac{1565}{2006}\right)\) \(e\left(\frac{253}{1003}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{838}{1003}\right)\)
\(\chi_{4013}(32,\cdot)\) 4013.l 4012 Yes \(-1\) \(1\) \(e\left(\frac{5}{4012}\right)\) \(e\left(\frac{701}{4012}\right)\) \(e\left(\frac{5}{2006}\right)\) \(e\left(\frac{3181}{4012}\right)\) \(e\left(\frac{353}{2006}\right)\) \(e\left(\frac{256}{1003}\right)\) \(e\left(\frac{15}{4012}\right)\) \(e\left(\frac{701}{2006}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{709}{1003}\right)\)