Properties

Modulus $6037$
Structure \(C_{6036}\)
Order $6036$

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6037)
 
pari: g = idealstar(,6037,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 6036
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{6036}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6037}(5,\cdot)$

First 32 of 6036 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{6037}(1,\cdot)\) 6037.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6037}(2,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{695}{2012}\right)\) \(e\left(\frac{445}{1006}\right)\) \(e\left(\frac{695}{1006}\right)\) \(e\left(\frac{495}{2012}\right)\) \(e\left(\frac{1585}{2012}\right)\) \(e\left(\frac{709}{2012}\right)\) \(e\left(\frac{73}{2012}\right)\) \(e\left(\frac{445}{503}\right)\) \(e\left(\frac{595}{1006}\right)\) \(e\left(\frac{409}{1006}\right)\)
\(\chi_{6037}(3,\cdot)\) 6037.k 3018 yes \(1\) \(1\) \(e\left(\frac{445}{1006}\right)\) \(e\left(\frac{1090}{1509}\right)\) \(e\left(\frac{445}{503}\right)\) \(e\left(\frac{133}{3018}\right)\) \(e\left(\frac{497}{3018}\right)\) \(e\left(\frac{577}{1006}\right)\) \(e\left(\frac{329}{1006}\right)\) \(e\left(\frac{671}{1509}\right)\) \(e\left(\frac{734}{1509}\right)\) \(e\left(\frac{479}{503}\right)\)
\(\chi_{6037}(4,\cdot)\) 6037.h 1006 yes \(1\) \(1\) \(e\left(\frac{695}{1006}\right)\) \(e\left(\frac{445}{503}\right)\) \(e\left(\frac{192}{503}\right)\) \(e\left(\frac{495}{1006}\right)\) \(e\left(\frac{579}{1006}\right)\) \(e\left(\frac{709}{1006}\right)\) \(e\left(\frac{73}{1006}\right)\) \(e\left(\frac{387}{503}\right)\) \(e\left(\frac{92}{503}\right)\) \(e\left(\frac{409}{503}\right)\)
\(\chi_{6037}(5,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{495}{2012}\right)\) \(e\left(\frac{133}{3018}\right)\) \(e\left(\frac{495}{1006}\right)\) \(e\left(\frac{1}{6036}\right)\) \(e\left(\frac{1751}{6036}\right)\) \(e\left(\frac{201}{2012}\right)\) \(e\left(\frac{1485}{2012}\right)\) \(e\left(\frac{133}{1509}\right)\) \(e\left(\frac{743}{3018}\right)\) \(e\left(\frac{465}{1006}\right)\)
\(\chi_{6037}(6,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1585}{2012}\right)\) \(e\left(\frac{497}{3018}\right)\) \(e\left(\frac{579}{1006}\right)\) \(e\left(\frac{1751}{6036}\right)\) \(e\left(\frac{5749}{6036}\right)\) \(e\left(\frac{1863}{2012}\right)\) \(e\left(\frac{731}{2012}\right)\) \(e\left(\frac{497}{1509}\right)\) \(e\left(\frac{235}{3018}\right)\) \(e\left(\frac{361}{1006}\right)\)
\(\chi_{6037}(7,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{709}{2012}\right)\) \(e\left(\frac{577}{1006}\right)\) \(e\left(\frac{709}{1006}\right)\) \(e\left(\frac{201}{2012}\right)\) \(e\left(\frac{1863}{2012}\right)\) \(e\left(\frac{483}{2012}\right)\) \(e\left(\frac{115}{2012}\right)\) \(e\left(\frac{74}{503}\right)\) \(e\left(\frac{455}{1006}\right)\) \(e\left(\frac{727}{1006}\right)\)
\(\chi_{6037}(8,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{73}{2012}\right)\) \(e\left(\frac{329}{1006}\right)\) \(e\left(\frac{73}{1006}\right)\) \(e\left(\frac{1485}{2012}\right)\) \(e\left(\frac{731}{2012}\right)\) \(e\left(\frac{115}{2012}\right)\) \(e\left(\frac{219}{2012}\right)\) \(e\left(\frac{329}{503}\right)\) \(e\left(\frac{779}{1006}\right)\) \(e\left(\frac{221}{1006}\right)\)
\(\chi_{6037}(9,\cdot)\) 6037.i 1509 yes \(1\) \(1\) \(e\left(\frac{445}{503}\right)\) \(e\left(\frac{671}{1509}\right)\) \(e\left(\frac{387}{503}\right)\) \(e\left(\frac{133}{1509}\right)\) \(e\left(\frac{497}{1509}\right)\) \(e\left(\frac{74}{503}\right)\) \(e\left(\frac{329}{503}\right)\) \(e\left(\frac{1342}{1509}\right)\) \(e\left(\frac{1468}{1509}\right)\) \(e\left(\frac{455}{503}\right)\)
\(\chi_{6037}(10,\cdot)\) 6037.k 3018 yes \(1\) \(1\) \(e\left(\frac{595}{1006}\right)\) \(e\left(\frac{734}{1509}\right)\) \(e\left(\frac{92}{503}\right)\) \(e\left(\frac{743}{3018}\right)\) \(e\left(\frac{235}{3018}\right)\) \(e\left(\frac{455}{1006}\right)\) \(e\left(\frac{779}{1006}\right)\) \(e\left(\frac{1468}{1509}\right)\) \(e\left(\frac{1264}{1509}\right)\) \(e\left(\frac{437}{503}\right)\)
\(\chi_{6037}(11,\cdot)\) 6037.h 1006 yes \(1\) \(1\) \(e\left(\frac{409}{1006}\right)\) \(e\left(\frac{479}{503}\right)\) \(e\left(\frac{409}{503}\right)\) \(e\left(\frac{465}{1006}\right)\) \(e\left(\frac{361}{1006}\right)\) \(e\left(\frac{727}{1006}\right)\) \(e\left(\frac{221}{1006}\right)\) \(e\left(\frac{455}{503}\right)\) \(e\left(\frac{437}{503}\right)\) \(e\left(\frac{308}{503}\right)\)
\(\chi_{6037}(12,\cdot)\) 6037.i 1509 yes \(1\) \(1\) \(e\left(\frac{67}{503}\right)\) \(e\left(\frac{916}{1509}\right)\) \(e\left(\frac{134}{503}\right)\) \(e\left(\frac{809}{1509}\right)\) \(e\left(\frac{1117}{1509}\right)\) \(e\left(\frac{140}{503}\right)\) \(e\left(\frac{201}{503}\right)\) \(e\left(\frac{323}{1509}\right)\) \(e\left(\frac{1010}{1509}\right)\) \(e\left(\frac{385}{503}\right)\)
\(\chi_{6037}(13,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1309}{2012}\right)\) \(e\left(\frac{1313}{3018}\right)\) \(e\left(\frac{303}{1006}\right)\) \(e\left(\frac{1031}{6036}\right)\) \(e\left(\frac{517}{6036}\right)\) \(e\left(\frac{2007}{2012}\right)\) \(e\left(\frac{1915}{2012}\right)\) \(e\left(\frac{1313}{1509}\right)\) \(e\left(\frac{2479}{3018}\right)\) \(e\left(\frac{559}{1006}\right)\)
\(\chi_{6037}(14,\cdot)\) 6037.g 503 yes \(1\) \(1\) \(e\left(\frac{351}{503}\right)\) \(e\left(\frac{8}{503}\right)\) \(e\left(\frac{199}{503}\right)\) \(e\left(\frac{174}{503}\right)\) \(e\left(\frac{359}{503}\right)\) \(e\left(\frac{298}{503}\right)\) \(e\left(\frac{47}{503}\right)\) \(e\left(\frac{16}{503}\right)\) \(e\left(\frac{22}{503}\right)\) \(e\left(\frac{65}{503}\right)\)
\(\chi_{6037}(15,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{1385}{2012}\right)\) \(e\left(\frac{771}{1006}\right)\) \(e\left(\frac{379}{1006}\right)\) \(e\left(\frac{89}{2012}\right)\) \(e\left(\frac{915}{2012}\right)\) \(e\left(\frac{1355}{2012}\right)\) \(e\left(\frac{131}{2012}\right)\) \(e\left(\frac{268}{503}\right)\) \(e\left(\frac{737}{1006}\right)\) \(e\left(\frac{417}{1006}\right)\)
\(\chi_{6037}(16,\cdot)\) 6037.g 503 yes \(1\) \(1\) \(e\left(\frac{192}{503}\right)\) \(e\left(\frac{387}{503}\right)\) \(e\left(\frac{384}{503}\right)\) \(e\left(\frac{495}{503}\right)\) \(e\left(\frac{76}{503}\right)\) \(e\left(\frac{206}{503}\right)\) \(e\left(\frac{73}{503}\right)\) \(e\left(\frac{271}{503}\right)\) \(e\left(\frac{184}{503}\right)\) \(e\left(\frac{315}{503}\right)\)
\(\chi_{6037}(17,\cdot)\) 6037.k 3018 yes \(1\) \(1\) \(e\left(\frac{469}{1006}\right)\) \(e\left(\frac{691}{1509}\right)\) \(e\left(\frac{469}{503}\right)\) \(e\left(\frac{1639}{3018}\right)\) \(e\left(\frac{2789}{3018}\right)\) \(e\left(\frac{477}{1006}\right)\) \(e\left(\frac{401}{1006}\right)\) \(e\left(\frac{1382}{1509}\right)\) \(e\left(\frac{14}{1509}\right)\) \(e\left(\frac{90}{503}\right)\)
\(\chi_{6037}(18,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{463}{2012}\right)\) \(e\left(\frac{2677}{3018}\right)\) \(e\left(\frac{463}{1006}\right)\) \(e\left(\frac{2017}{6036}\right)\) \(e\left(\frac{707}{6036}\right)\) \(e\left(\frac{1005}{2012}\right)\) \(e\left(\frac{1389}{2012}\right)\) \(e\left(\frac{1168}{1509}\right)\) \(e\left(\frac{1703}{3018}\right)\) \(e\left(\frac{313}{1006}\right)\)
\(\chi_{6037}(19,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{721}{2012}\right)\) \(e\left(\frac{259}{1006}\right)\) \(e\left(\frac{721}{1006}\right)\) \(e\left(\frac{1961}{2012}\right)\) \(e\left(\frac{1239}{2012}\right)\) \(e\left(\frac{1439}{2012}\right)\) \(e\left(\frac{151}{2012}\right)\) \(e\left(\frac{259}{503}\right)\) \(e\left(\frac{335}{1006}\right)\) \(e\left(\frac{281}{1006}\right)\)
\(\chi_{6037}(20,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1885}{2012}\right)\) \(e\left(\frac{2803}{3018}\right)\) \(e\left(\frac{879}{1006}\right)\) \(e\left(\frac{2971}{6036}\right)\) \(e\left(\frac{5225}{6036}\right)\) \(e\left(\frac{1619}{2012}\right)\) \(e\left(\frac{1631}{2012}\right)\) \(e\left(\frac{1294}{1509}\right)\) \(e\left(\frac{1295}{3018}\right)\) \(e\left(\frac{277}{1006}\right)\)
\(\chi_{6037}(21,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1599}{2012}\right)\) \(e\left(\frac{893}{3018}\right)\) \(e\left(\frac{593}{1006}\right)\) \(e\left(\frac{869}{6036}\right)\) \(e\left(\frac{547}{6036}\right)\) \(e\left(\frac{1637}{2012}\right)\) \(e\left(\frac{773}{2012}\right)\) \(e\left(\frac{893}{1509}\right)\) \(e\left(\frac{2833}{3018}\right)\) \(e\left(\frac{679}{1006}\right)\)
\(\chi_{6037}(22,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{1513}{2012}\right)\) \(e\left(\frac{397}{1006}\right)\) \(e\left(\frac{507}{1006}\right)\) \(e\left(\frac{1425}{2012}\right)\) \(e\left(\frac{295}{2012}\right)\) \(e\left(\frac{151}{2012}\right)\) \(e\left(\frac{515}{2012}\right)\) \(e\left(\frac{397}{503}\right)\) \(e\left(\frac{463}{1006}\right)\) \(e\left(\frac{19}{1006}\right)\)
\(\chi_{6037}(23,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1435}{2012}\right)\) \(e\left(\frac{1859}{3018}\right)\) \(e\left(\frac{429}{1006}\right)\) \(e\left(\frac{5165}{6036}\right)\) \(e\left(\frac{1987}{6036}\right)\) \(e\left(\frac{1985}{2012}\right)\) \(e\left(\frac{281}{2012}\right)\) \(e\left(\frac{350}{1509}\right)\) \(e\left(\frac{1717}{3018}\right)\) \(e\left(\frac{403}{1006}\right)\)
\(\chi_{6037}(24,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{963}{2012}\right)\) \(e\left(\frac{149}{3018}\right)\) \(e\left(\frac{963}{1006}\right)\) \(e\left(\frac{4721}{6036}\right)\) \(e\left(\frac{3187}{6036}\right)\) \(e\left(\frac{1269}{2012}\right)\) \(e\left(\frac{877}{2012}\right)\) \(e\left(\frac{149}{1509}\right)\) \(e\left(\frac{787}{3018}\right)\) \(e\left(\frac{173}{1006}\right)\)
\(\chi_{6037}(25,\cdot)\) 6037.k 3018 yes \(1\) \(1\) \(e\left(\frac{495}{1006}\right)\) \(e\left(\frac{133}{1509}\right)\) \(e\left(\frac{495}{503}\right)\) \(e\left(\frac{1}{3018}\right)\) \(e\left(\frac{1751}{3018}\right)\) \(e\left(\frac{201}{1006}\right)\) \(e\left(\frac{479}{1006}\right)\) \(e\left(\frac{266}{1509}\right)\) \(e\left(\frac{743}{1509}\right)\) \(e\left(\frac{465}{503}\right)\)
\(\chi_{6037}(26,\cdot)\) 6037.i 1509 yes \(1\) \(1\) \(e\left(\frac{501}{503}\right)\) \(e\left(\frac{1324}{1509}\right)\) \(e\left(\frac{499}{503}\right)\) \(e\left(\frac{629}{1509}\right)\) \(e\left(\frac{1318}{1509}\right)\) \(e\left(\frac{176}{503}\right)\) \(e\left(\frac{497}{503}\right)\) \(e\left(\frac{1139}{1509}\right)\) \(e\left(\frac{623}{1509}\right)\) \(e\left(\frac{484}{503}\right)\)
\(\chi_{6037}(27,\cdot)\) 6037.h 1006 yes \(1\) \(1\) \(e\left(\frac{329}{1006}\right)\) \(e\left(\frac{84}{503}\right)\) \(e\left(\frac{329}{503}\right)\) \(e\left(\frac{133}{1006}\right)\) \(e\left(\frac{497}{1006}\right)\) \(e\left(\frac{725}{1006}\right)\) \(e\left(\frac{987}{1006}\right)\) \(e\left(\frac{168}{503}\right)\) \(e\left(\frac{231}{503}\right)\) \(e\left(\frac{431}{503}\right)\)
\(\chi_{6037}(28,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{87}{2012}\right)\) \(e\left(\frac{461}{1006}\right)\) \(e\left(\frac{87}{1006}\right)\) \(e\left(\frac{1191}{2012}\right)\) \(e\left(\frac{1009}{2012}\right)\) \(e\left(\frac{1901}{2012}\right)\) \(e\left(\frac{261}{2012}\right)\) \(e\left(\frac{461}{503}\right)\) \(e\left(\frac{639}{1006}\right)\) \(e\left(\frac{539}{1006}\right)\)
\(\chi_{6037}(29,\cdot)\) 6037.i 1509 yes \(1\) \(1\) \(e\left(\frac{359}{503}\right)\) \(e\left(\frac{1267}{1509}\right)\) \(e\left(\frac{215}{503}\right)\) \(e\left(\frac{521}{1509}\right)\) \(e\left(\frac{835}{1509}\right)\) \(e\left(\frac{97}{503}\right)\) \(e\left(\frac{71}{503}\right)\) \(e\left(\frac{1025}{1509}\right)\) \(e\left(\frac{89}{1509}\right)\) \(e\left(\frac{141}{503}\right)\)
\(\chi_{6037}(30,\cdot)\) 6037.g 503 yes \(1\) \(1\) \(e\left(\frac{17}{503}\right)\) \(e\left(\frac{105}{503}\right)\) \(e\left(\frac{34}{503}\right)\) \(e\left(\frac{146}{503}\right)\) \(e\left(\frac{122}{503}\right)\) \(e\left(\frac{13}{503}\right)\) \(e\left(\frac{51}{503}\right)\) \(e\left(\frac{210}{503}\right)\) \(e\left(\frac{163}{503}\right)\) \(e\left(\frac{413}{503}\right)\)
\(\chi_{6037}(31,\cdot)\) 6037.l 6036 yes \(-1\) \(1\) \(e\left(\frac{1403}{2012}\right)\) \(e\left(\frac{379}{3018}\right)\) \(e\left(\frac{397}{1006}\right)\) \(e\left(\frac{3157}{6036}\right)\) \(e\left(\frac{4967}{6036}\right)\) \(e\left(\frac{777}{2012}\right)\) \(e\left(\frac{185}{2012}\right)\) \(e\left(\frac{379}{1509}\right)\) \(e\left(\frac{665}{3018}\right)\) \(e\left(\frac{251}{1006}\right)\)
\(\chi_{6037}(32,\cdot)\) 6037.j 2012 yes \(-1\) \(1\) \(e\left(\frac{1463}{2012}\right)\) \(e\left(\frac{213}{1006}\right)\) \(e\left(\frac{457}{1006}\right)\) \(e\left(\frac{463}{2012}\right)\) \(e\left(\frac{1889}{2012}\right)\) \(e\left(\frac{1533}{2012}\right)\) \(e\left(\frac{365}{2012}\right)\) \(e\left(\frac{213}{503}\right)\) \(e\left(\frac{963}{1006}\right)\) \(e\left(\frac{33}{1006}\right)\)
Click here to search among the remaining 6004 characters.