Properties

 Modulus 6017 Structure $$C_{2730}\times C_{2}$$ Order 5460

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(6017)

pari: g = idealstar(,6017,2)

Character group

 sage: G.order()  pari: g.no Order = 5460 sage: H.invariants()  pari: g.cyc Structure = $$C_{2730}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6017}(3284,\cdot)$, $\chi_{6017}(4377,\cdot)$

First 32 of 5460 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 12
$$\chi_{6017}(1,\cdot)$$ 6017.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6017}(2,\cdot)$$ 6017.cl 2730 yes $$1$$ $$1$$ $$e\left(\frac{139}{1365}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{278}{1365}\right)$$ $$e\left(\frac{1987}{2730}\right)$$ $$e\left(\frac{1877}{2730}\right)$$ $$e\left(\frac{1213}{1365}\right)$$ $$e\left(\frac{139}{455}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{151}{182}\right)$$ $$e\left(\frac{431}{546}\right)$$
$$\chi_{6017}(3,\cdot)$$ 6017.bf 70 yes $$-1$$ $$1$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{33}{70}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{6017}(4,\cdot)$$ 6017.ci 1365 yes $$1$$ $$1$$ $$e\left(\frac{278}{1365}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{556}{1365}\right)$$ $$e\left(\frac{622}{1365}\right)$$ $$e\left(\frac{512}{1365}\right)$$ $$e\left(\frac{1061}{1365}\right)$$ $$e\left(\frac{278}{455}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{60}{91}\right)$$ $$e\left(\frac{158}{273}\right)$$
$$\chi_{6017}(5,\cdot)$$ 6017.cj 2730 yes $$-1$$ $$1$$ $$e\left(\frac{1987}{2730}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{622}{1365}\right)$$ $$e\left(\frac{773}{2730}\right)$$ $$e\left(\frac{779}{1365}\right)$$ $$e\left(\frac{1549}{2730}\right)$$ $$e\left(\frac{167}{910}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{1}{91}\right)$$ $$e\left(\frac{163}{546}\right)$$
$$\chi_{6017}(6,\cdot)$$ 6017.ck 2730 yes $$-1$$ $$1$$ $$e\left(\frac{1877}{2730}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{512}{1365}\right)$$ $$e\left(\frac{779}{1365}\right)$$ $$e\left(\frac{2033}{2730}\right)$$ $$e\left(\frac{1139}{2730}\right)$$ $$e\left(\frac{57}{910}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{47}{182}\right)$$ $$e\left(\frac{118}{273}\right)$$
$$\chi_{6017}(7,\cdot)$$ 6017.cl 2730 yes $$1$$ $$1$$ $$e\left(\frac{1213}{1365}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{1061}{1365}\right)$$ $$e\left(\frac{1549}{2730}\right)$$ $$e\left(\frac{1139}{2730}\right)$$ $$e\left(\frac{451}{1365}\right)$$ $$e\left(\frac{303}{455}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{83}{182}\right)$$ $$e\left(\frac{167}{546}\right)$$
$$\chi_{6017}(8,\cdot)$$ 6017.cf 910 yes $$1$$ $$1$$ $$e\left(\frac{139}{455}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{278}{455}\right)$$ $$e\left(\frac{167}{910}\right)$$ $$e\left(\frac{57}{910}\right)$$ $$e\left(\frac{303}{455}\right)$$ $$e\left(\frac{417}{455}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{89}{182}\right)$$ $$e\left(\frac{67}{182}\right)$$
$$\chi_{6017}(9,\cdot)$$ 6017.z 35 yes $$1$$ $$1$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{6017}(10,\cdot)$$ 6017.bq 182 yes $$-1$$ $$1$$ $$e\left(\frac{151}{182}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{60}{91}\right)$$ $$e\left(\frac{1}{91}\right)$$ $$e\left(\frac{47}{182}\right)$$ $$e\left(\frac{83}{182}\right)$$ $$e\left(\frac{89}{182}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{153}{182}\right)$$ $$e\left(\frac{8}{91}\right)$$
$$\chi_{6017}(12,\cdot)$$ 6017.ce 546 no $$-1$$ $$1$$ $$e\left(\frac{431}{546}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{158}{273}\right)$$ $$e\left(\frac{163}{546}\right)$$ $$e\left(\frac{118}{273}\right)$$ $$e\left(\frac{167}{546}\right)$$ $$e\left(\frac{67}{182}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{8}{91}\right)$$ $$e\left(\frac{121}{546}\right)$$
$$\chi_{6017}(13,\cdot)$$ 6017.bw 210 yes $$-1$$ $$1$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{17}{105}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{137}{210}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{6017}(14,\cdot)$$ 6017.bm 105 yes $$1$$ $$1$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{31}{105}\right)$$ $$e\left(\frac{11}{105}\right)$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{6017}(15,\cdot)$$ 6017.ci 1365 yes $$1$$ $$1$$ $$e\left(\frac{428}{1365}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{856}{1365}\right)$$ $$e\left(\frac{172}{1365}\right)$$ $$e\left(\frac{857}{1365}\right)$$ $$e\left(\frac{131}{1365}\right)$$ $$e\left(\frac{428}{455}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{40}{91}\right)$$ $$e\left(\frac{257}{273}\right)$$
$$\chi_{6017}(16,\cdot)$$ 6017.ci 1365 yes $$1$$ $$1$$ $$e\left(\frac{556}{1365}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{1112}{1365}\right)$$ $$e\left(\frac{1244}{1365}\right)$$ $$e\left(\frac{1024}{1365}\right)$$ $$e\left(\frac{757}{1365}\right)$$ $$e\left(\frac{101}{455}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{29}{91}\right)$$ $$e\left(\frac{43}{273}\right)$$
$$\chi_{6017}(17,\cdot)$$ 6017.cl 2730 yes $$1$$ $$1$$ $$e\left(\frac{241}{1365}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{482}{1365}\right)$$ $$e\left(\frac{283}{2730}\right)$$ $$e\left(\frac{53}{2730}\right)$$ $$e\left(\frac{1072}{1365}\right)$$ $$e\left(\frac{241}{455}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{51}{182}\right)$$ $$e\left(\frac{107}{546}\right)$$
$$\chi_{6017}(18,\cdot)$$ 6017.cl 2730 yes $$1$$ $$1$$ $$e\left(\frac{373}{1365}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{746}{1365}\right)$$ $$e\left(\frac{1129}{2730}\right)$$ $$e\left(\frac{2189}{2730}\right)$$ $$e\left(\frac{1291}{1365}\right)$$ $$e\left(\frac{373}{455}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{125}{182}\right)$$ $$e\left(\frac{41}{546}\right)$$
$$\chi_{6017}(19,\cdot)$$ 6017.ck 2730 yes $$-1$$ $$1$$ $$e\left(\frac{1969}{2730}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{604}{1365}\right)$$ $$e\left(\frac{823}{1365}\right)$$ $$e\left(\frac{2281}{2730}\right)$$ $$e\left(\frac{1333}{2730}\right)$$ $$e\left(\frac{149}{910}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{59}{182}\right)$$ $$e\left(\frac{152}{273}\right)$$
$$\chi_{6017}(20,\cdot)$$ 6017.cj 2730 yes $$-1$$ $$1$$ $$e\left(\frac{2543}{2730}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{1178}{1365}\right)$$ $$e\left(\frac{2017}{2730}\right)$$ $$e\left(\frac{1291}{1365}\right)$$ $$e\left(\frac{941}{2730}\right)$$ $$e\left(\frac{723}{910}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{61}{91}\right)$$ $$e\left(\frac{479}{546}\right)$$
$$\chi_{6017}(21,\cdot)$$ 6017.bj 78 yes $$-1$$ $$1$$ $$e\left(\frac{37}{78}\right)$$ $$1$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{37}{39}\right)$$
$$\chi_{6017}(23,\cdot)$$ 6017.ce 546 no $$-1$$ $$1$$ $$e\left(\frac{293}{546}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{20}{273}\right)$$ $$e\left(\frac{31}{546}\right)$$ $$e\left(\frac{205}{273}\right)$$ $$e\left(\frac{149}{546}\right)$$ $$e\left(\frac{111}{182}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{54}{91}\right)$$ $$e\left(\frac{157}{546}\right)$$
$$\chi_{6017}(24,\cdot)$$ 6017.ch 910 yes $$-1$$ $$1$$ $$e\left(\frac{811}{910}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{356}{455}\right)$$ $$e\left(\frac{12}{455}\right)$$ $$e\left(\frac{109}{910}\right)$$ $$e\left(\frac{177}{910}\right)$$ $$e\left(\frac{613}{910}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{167}{182}\right)$$ $$e\left(\frac{1}{91}\right)$$
$$\chi_{6017}(25,\cdot)$$ 6017.ci 1365 yes $$1$$ $$1$$ $$e\left(\frac{622}{1365}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{1244}{1365}\right)$$ $$e\left(\frac{773}{1365}\right)$$ $$e\left(\frac{193}{1365}\right)$$ $$e\left(\frac{184}{1365}\right)$$ $$e\left(\frac{167}{455}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{2}{91}\right)$$ $$e\left(\frac{163}{273}\right)$$
$$\chi_{6017}(26,\cdot)$$ 6017.ca 390 yes $$-1$$ $$1$$ $$e\left(\frac{283}{390}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{88}{195}\right)$$ $$e\left(\frac{347}{390}\right)$$ $$e\left(\frac{161}{195}\right)$$ $$e\left(\frac{211}{390}\right)$$ $$e\left(\frac{23}{130}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{43}{78}\right)$$
$$\chi_{6017}(27,\cdot)$$ 6017.bf 70 yes $$-1$$ $$1$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{6017}(28,\cdot)$$ 6017.bp 130 yes $$1$$ $$1$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{3}{130}\right)$$ $$e\left(\frac{103}{130}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{6017}(29,\cdot)$$ 6017.ch 910 yes $$-1$$ $$1$$ $$e\left(\frac{257}{910}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{257}{455}\right)$$ $$e\left(\frac{24}{455}\right)$$ $$e\left(\frac{673}{910}\right)$$ $$e\left(\frac{809}{910}\right)$$ $$e\left(\frac{771}{910}\right)$$ $$e\left(\frac{32}{35}\right)$$ $$e\left(\frac{61}{182}\right)$$ $$e\left(\frac{2}{91}\right)$$
$$\chi_{6017}(30,\cdot)$$ 6017.bp 130 yes $$1$$ $$1$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{6017}(31,\cdot)$$ 6017.cg 910 yes $$-1$$ $$1$$ $$e\left(\frac{141}{910}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{141}{455}\right)$$ $$e\left(\frac{669}{910}\right)$$ $$e\left(\frac{12}{455}\right)$$ $$e\left(\frac{327}{910}\right)$$ $$e\left(\frac{423}{910}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{81}{91}\right)$$ $$e\left(\frac{33}{182}\right)$$
$$\chi_{6017}(32,\cdot)$$ 6017.cc 546 yes $$1$$ $$1$$ $$e\left(\frac{139}{273}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{273}\right)$$ $$e\left(\frac{349}{546}\right)$$ $$e\left(\frac{239}{546}\right)$$ $$e\left(\frac{121}{273}\right)$$ $$e\left(\frac{48}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{27}{182}\right)$$ $$e\left(\frac{517}{546}\right)$$
$$\chi_{6017}(34,\cdot)$$ 6017.bx 273 no $$1$$ $$1$$ $$e\left(\frac{76}{273}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{152}{273}\right)$$ $$e\left(\frac{227}{273}\right)$$ $$e\left(\frac{193}{273}\right)$$ $$e\left(\frac{184}{273}\right)$$ $$e\left(\frac{76}{91}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{10}{91}\right)$$ $$e\left(\frac{269}{273}\right)$$
$$\chi_{6017}(35,\cdot)$$ 6017.ch 910 yes $$-1$$ $$1$$ $$e\left(\frac{561}{910}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{106}{455}\right)$$ $$e\left(\frac{387}{455}\right)$$ $$e\left(\frac{899}{910}\right)$$ $$e\left(\frac{817}{910}\right)$$ $$e\left(\frac{773}{910}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{85}{182}\right)$$ $$e\left(\frac{55}{91}\right)$$