# Properties

 Modulus $6001$ Structure $$C_{352}\times C_{16}$$ Order $5632$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(6001)

pari: g = idealstar(,6001,2)

## Character group

 sage: G.order()  pari: g.no Order = 5632 sage: H.invariants()  pari: g.cyc Structure = $$C_{352}\times C_{16}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6001}(2825,\cdot)$, $\chi_{6001}(3180,\cdot)$

## First 32 of 5632 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{6001}(1,\cdot)$$ 6001.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6001}(2,\cdot)$$ 6001.dc 88 yes $$1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$1$$ $$e\left(\frac{7}{88}\right)$$
$$\chi_{6001}(3,\cdot)$$ 6001.er 352 yes $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{23}{352}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{67}{352}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{23}{176}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{107}{176}\right)$$
$$\chi_{6001}(4,\cdot)$$ 6001.ct 44 yes $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$1$$ $$e\left(\frac{7}{44}\right)$$
$$\chi_{6001}(5,\cdot)$$ 6001.er 352 yes $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{67}{352}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{287}{352}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{67}{176}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{151}{176}\right)$$
$$\chi_{6001}(6,\cdot)$$ 6001.cm 32 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$1$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{6001}(7,\cdot)$$ 6001.cd 32 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{31}{32}\right)$$ $$-1$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{6001}(8,\cdot)$$ 6001.dc 88 yes $$1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$1$$ $$i$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$1$$ $$e\left(\frac{21}{88}\right)$$
$$\chi_{6001}(9,\cdot)$$ 6001.ec 176 yes $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{23}{176}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{67}{176}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{23}{88}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{88}\right)$$
$$\chi_{6001}(10,\cdot)$$ 6001.cn 32 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{17}{32}\right)$$ $$1$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{6001}(11,\cdot)$$ 6001.do 176 yes $$-1$$ $$1$$ $$e\left(\frac{7}{88}\right)$$ $$e\left(\frac{107}{176}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{151}{176}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{21}{88}\right)$$ $$e\left(\frac{19}{88}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{51}{176}\right)$$
$$\chi_{6001}(12,\cdot)$$ 6001.ep 352 yes $$1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{263}{352}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{307}{352}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{87}{176}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{135}{176}\right)$$
$$\chi_{6001}(13,\cdot)$$ 6001.ej 352 yes $$-1$$ $$1$$ $$e\left(\frac{45}{88}\right)$$ $$e\left(\frac{73}{352}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{29}{352}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{47}{88}\right)$$ $$e\left(\frac{73}{176}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{17}{88}\right)$$
$$\chi_{6001}(14,\cdot)$$ 6001.es 352 yes $$1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{109}{352}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{241}{352}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{109}{176}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{135}{176}\right)$$
$$\chi_{6001}(15,\cdot)$$ 6001.ec 176 yes $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{45}{176}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{176}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{45}{88}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{41}{88}\right)$$
$$\chi_{6001}(16,\cdot)$$ 6001.bv 22 yes $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$1$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{6001}(18,\cdot)$$ 6001.dy 176 no $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{83}{176}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{127}{176}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{83}{88}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{44}\right)$$
$$\chi_{6001}(19,\cdot)$$ 6001.ed 176 yes $$1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{13}{176}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{145}{176}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{88}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{88}\right)$$
$$\chi_{6001}(20,\cdot)$$ 6001.ep 352 yes $$1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{307}{352}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{175}{352}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{131}{176}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{3}{176}\right)$$
$$\chi_{6001}(21,\cdot)$$ 6001.cv 88 yes $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{3}{88}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{47}{88}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{44}\right)$$
$$\chi_{6001}(22,\cdot)$$ 6001.dn 176 yes $$-1$$ $$1$$ $$e\left(\frac{65}{88}\right)$$ $$e\left(\frac{167}{176}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{35}{176}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{19}{88}\right)$$ $$e\left(\frac{79}{88}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{65}{176}\right)$$
$$\chi_{6001}(23,\cdot)$$ 6001.eb 176 yes $$-1$$ $$1$$ $$e\left(\frac{81}{88}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{67}{88}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{103}{176}\right)$$
$$\chi_{6001}(24,\cdot)$$ 6001.et 352 yes $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{31}{352}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{75}{352}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{31}{176}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{149}{176}\right)$$
$$\chi_{6001}(25,\cdot)$$ 6001.ec 176 yes $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{67}{176}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{111}{176}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{67}{88}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{63}{88}\right)$$
$$\chi_{6001}(26,\cdot)$$ 6001.eg 352 yes $$-1$$ $$1$$ $$e\left(\frac{15}{88}\right)$$ $$e\left(\frac{193}{352}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{149}{352}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{45}{88}\right)$$ $$e\left(\frac{17}{176}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{6001}(27,\cdot)$$ 6001.er 352 yes $$1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{69}{352}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{201}{352}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{69}{176}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{145}{176}\right)$$
$$\chi_{6001}(28,\cdot)$$ 6001.ep 352 yes $$1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{229}{352}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{352}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{53}{176}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{149}{176}\right)$$
$$\chi_{6001}(29,\cdot)$$ 6001.dq 176 yes $$-1$$ $$1$$ $$e\left(\frac{5}{88}\right)$$ $$e\left(\frac{45}{176}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{1}{176}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{88}\right)$$ $$e\left(\frac{45}{88}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{49}{176}\right)$$
$$\chi_{6001}(30,\cdot)$$ 6001.dx 176 yes $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{105}{176}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{176}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{88}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{6001}(31,\cdot)$$ 6001.eq 352 yes $$1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{291}{352}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{159}{352}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{115}{176}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{139}{176}\right)$$
$$\chi_{6001}(32,\cdot)$$ 6001.dc 88 yes $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$1$$ $$e\left(\frac{35}{88}\right)$$
$$\chi_{6001}(33,\cdot)$$ 6001.em 352 yes $$-1$$ $$1$$ $$e\left(\frac{37}{88}\right)$$ $$e\left(\frac{237}{352}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{17}{352}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{23}{88}\right)$$ $$e\left(\frac{61}{176}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{79}{88}\right)$$