# Properties

 Modulus $3381$ Structure $$C_{2}\times C_{2}\times C_{462}$$ Order $1848$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3381)

pari: g = idealstar(,3381,2)

## Character group

 sage: G.order()  pari: g.no Order = 1848 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{462}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3381}(2255,\cdot)$, $\chi_{3381}(346,\cdot)$, $\chi_{3381}(442,\cdot)$

## First 32 of 1848 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$
$$\chi_{3381}(1,\cdot)$$ 3381.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3381}(2,\cdot)$$ 3381.cl 462 yes $$-1$$ $$1$$ $$e\left(\frac{359}{462}\right)$$ $$e\left(\frac{128}{231}\right)$$ $$e\left(\frac{251}{462}\right)$$ $$e\left(\frac{51}{154}\right)$$ $$e\left(\frac{74}{231}\right)$$ $$e\left(\frac{37}{462}\right)$$ $$e\left(\frac{54}{77}\right)$$ $$e\left(\frac{25}{231}\right)$$ $$e\left(\frac{283}{462}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{3381}(4,\cdot)$$ 3381.ce 231 no $$1$$ $$1$$ $$e\left(\frac{128}{231}\right)$$ $$e\left(\frac{25}{231}\right)$$ $$e\left(\frac{20}{231}\right)$$ $$e\left(\frac{51}{77}\right)$$ $$e\left(\frac{148}{231}\right)$$ $$e\left(\frac{37}{231}\right)$$ $$e\left(\frac{31}{77}\right)$$ $$e\left(\frac{50}{231}\right)$$ $$e\left(\frac{52}{231}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{3381}(5,\cdot)$$ 3381.ck 462 yes $$-1$$ $$1$$ $$e\left(\frac{251}{462}\right)$$ $$e\left(\frac{20}{231}\right)$$ $$e\left(\frac{263}{462}\right)$$ $$e\left(\frac{97}{154}\right)$$ $$e\left(\frac{26}{231}\right)$$ $$e\left(\frac{122}{231}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{40}{231}\right)$$ $$e\left(\frac{37}{462}\right)$$ $$e\left(\frac{28}{33}\right)$$
$$\chi_{3381}(8,\cdot)$$ 3381.bx 154 yes $$-1$$ $$1$$ $$e\left(\frac{51}{154}\right)$$ $$e\left(\frac{51}{77}\right)$$ $$e\left(\frac{97}{154}\right)$$ $$e\left(\frac{153}{154}\right)$$ $$e\left(\frac{74}{77}\right)$$ $$e\left(\frac{37}{154}\right)$$ $$e\left(\frac{8}{77}\right)$$ $$e\left(\frac{25}{77}\right)$$ $$e\left(\frac{129}{154}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{3381}(10,\cdot)$$ 3381.cf 462 no $$1$$ $$1$$ $$e\left(\frac{74}{231}\right)$$ $$e\left(\frac{148}{231}\right)$$ $$e\left(\frac{26}{231}\right)$$ $$e\left(\frac{74}{77}\right)$$ $$e\left(\frac{100}{231}\right)$$ $$e\left(\frac{281}{462}\right)$$ $$e\left(\frac{19}{154}\right)$$ $$e\left(\frac{65}{231}\right)$$ $$e\left(\frac{160}{231}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{3381}(11,\cdot)$$ 3381.ci 462 yes $$1$$ $$1$$ $$e\left(\frac{37}{462}\right)$$ $$e\left(\frac{37}{231}\right)$$ $$e\left(\frac{122}{231}\right)$$ $$e\left(\frac{37}{154}\right)$$ $$e\left(\frac{281}{462}\right)$$ $$e\left(\frac{64}{231}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{74}{231}\right)$$ $$e\left(\frac{40}{231}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{3381}(13,\cdot)$$ 3381.cc 154 no $$-1$$ $$1$$ $$e\left(\frac{54}{77}\right)$$ $$e\left(\frac{31}{77}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{8}{77}\right)$$ $$e\left(\frac{19}{154}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{129}{154}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{15}{154}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{3381}(16,\cdot)$$ 3381.ce 231 no $$1$$ $$1$$ $$e\left(\frac{25}{231}\right)$$ $$e\left(\frac{50}{231}\right)$$ $$e\left(\frac{40}{231}\right)$$ $$e\left(\frac{25}{77}\right)$$ $$e\left(\frac{65}{231}\right)$$ $$e\left(\frac{74}{231}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{100}{231}\right)$$ $$e\left(\frac{104}{231}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{3381}(17,\cdot)$$ 3381.ck 462 yes $$-1$$ $$1$$ $$e\left(\frac{283}{462}\right)$$ $$e\left(\frac{52}{231}\right)$$ $$e\left(\frac{37}{462}\right)$$ $$e\left(\frac{129}{154}\right)$$ $$e\left(\frac{160}{231}\right)$$ $$e\left(\frac{40}{231}\right)$$ $$e\left(\frac{15}{154}\right)$$ $$e\left(\frac{104}{231}\right)$$ $$e\left(\frac{281}{462}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{3381}(19,\cdot)$$ 3381.bv 66 no $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{3381}(20,\cdot)$$ 3381.by 154 yes $$-1$$ $$1$$ $$e\left(\frac{15}{154}\right)$$ $$e\left(\frac{15}{77}\right)$$ $$e\left(\frac{101}{154}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{53}{77}\right)$$ $$e\left(\frac{127}{154}\right)$$ $$e\left(\frac{30}{77}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{3381}(22,\cdot)$$ 3381.u 14 no $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$
$$\chi_{3381}(25,\cdot)$$ 3381.ce 231 no $$1$$ $$1$$ $$e\left(\frac{20}{231}\right)$$ $$e\left(\frac{40}{231}\right)$$ $$e\left(\frac{32}{231}\right)$$ $$e\left(\frac{20}{77}\right)$$ $$e\left(\frac{52}{231}\right)$$ $$e\left(\frac{13}{231}\right)$$ $$e\left(\frac{65}{77}\right)$$ $$e\left(\frac{80}{231}\right)$$ $$e\left(\frac{37}{231}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{3381}(26,\cdot)$$ 3381.cj 462 yes $$1$$ $$1$$ $$e\left(\frac{221}{462}\right)$$ $$e\left(\frac{221}{231}\right)$$ $$e\left(\frac{223}{231}\right)$$ $$e\left(\frac{67}{154}\right)$$ $$e\left(\frac{205}{462}\right)$$ $$e\left(\frac{109}{462}\right)$$ $$e\left(\frac{83}{154}\right)$$ $$e\left(\frac{211}{231}\right)$$ $$e\left(\frac{164}{231}\right)$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{3381}(29,\cdot)$$ 3381.bx 154 yes $$-1$$ $$1$$ $$e\left(\frac{43}{154}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{129}{154}\right)$$ $$e\left(\frac{2}{77}\right)$$ $$e\left(\frac{1}{154}\right)$$ $$e\left(\frac{46}{77}\right)$$ $$e\left(\frac{9}{77}\right)$$ $$e\left(\frac{145}{154}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{3381}(31,\cdot)$$ 3381.bu 66 no $$-1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{3381}(32,\cdot)$$ 3381.cl 462 yes $$-1$$ $$1$$ $$e\left(\frac{409}{462}\right)$$ $$e\left(\frac{178}{231}\right)$$ $$e\left(\frac{331}{462}\right)$$ $$e\left(\frac{101}{154}\right)$$ $$e\left(\frac{139}{231}\right)$$ $$e\left(\frac{185}{462}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{125}{231}\right)$$ $$e\left(\frac{29}{462}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{3381}(34,\cdot)$$ 3381.cd 154 no $$1$$ $$1$$ $$e\left(\frac{30}{77}\right)$$ $$e\left(\frac{60}{77}\right)$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{13}{77}\right)$$ $$e\left(\frac{1}{77}\right)$$ $$e\left(\frac{39}{154}\right)$$ $$e\left(\frac{123}{154}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{17}{77}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{3381}(37,\cdot)$$ 3381.ch 462 no $$-1$$ $$1$$ $$e\left(\frac{166}{231}\right)$$ $$e\left(\frac{101}{231}\right)$$ $$e\left(\frac{23}{462}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{355}{462}\right)$$ $$e\left(\frac{31}{462}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{202}{231}\right)$$ $$e\left(\frac{337}{462}\right)$$ $$e\left(\frac{65}{66}\right)$$
$$\chi_{3381}(38,\cdot)$$ 3381.ck 462 yes $$-1$$ $$1$$ $$e\left(\frac{373}{462}\right)$$ $$e\left(\frac{142}{231}\right)$$ $$e\left(\frac{181}{462}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{46}{231}\right)$$ $$e\left(\frac{127}{231}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{53}{231}\right)$$ $$e\left(\frac{101}{462}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{3381}(40,\cdot)$$ 3381.cf 462 no $$1$$ $$1$$ $$e\left(\frac{202}{231}\right)$$ $$e\left(\frac{173}{231}\right)$$ $$e\left(\frac{46}{231}\right)$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{17}{231}\right)$$ $$e\left(\frac{355}{462}\right)$$ $$e\left(\frac{81}{154}\right)$$ $$e\left(\frac{115}{231}\right)$$ $$e\left(\frac{212}{231}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{3381}(41,\cdot)$$ 3381.bz 154 yes $$1$$ $$1$$ $$e\left(\frac{135}{154}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{31}{77}\right)$$ $$e\left(\frac{97}{154}\right)$$ $$e\left(\frac{43}{154}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{19}{77}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{3381}(43,\cdot)$$ 3381.cb 154 no $$-1$$ $$1$$ $$e\left(\frac{13}{77}\right)$$ $$e\left(\frac{26}{77}\right)$$ $$e\left(\frac{57}{154}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{83}{154}\right)$$ $$e\left(\frac{117}{154}\right)$$ $$e\left(\frac{69}{77}\right)$$ $$e\left(\frac{52}{77}\right)$$ $$e\left(\frac{25}{154}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{3381}(44,\cdot)$$ 3381.ci 462 yes $$1$$ $$1$$ $$e\left(\frac{293}{462}\right)$$ $$e\left(\frac{62}{231}\right)$$ $$e\left(\frac{142}{231}\right)$$ $$e\left(\frac{139}{154}\right)$$ $$e\left(\frac{115}{462}\right)$$ $$e\left(\frac{101}{231}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{124}{231}\right)$$ $$e\left(\frac{92}{231}\right)$$ $$e\left(\frac{35}{66}\right)$$
$$\chi_{3381}(47,\cdot)$$ 3381.bk 42 no $$1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3381}(50,\cdot)$$ 3381.bg 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{3381}(52,\cdot)$$ 3381.cg 462 no $$-1$$ $$1$$ $$e\left(\frac{59}{231}\right)$$ $$e\left(\frac{118}{231}\right)$$ $$e\left(\frac{235}{462}\right)$$ $$e\left(\frac{59}{77}\right)$$ $$e\left(\frac{353}{462}\right)$$ $$e\left(\frac{73}{231}\right)$$ $$e\left(\frac{37}{154}\right)$$ $$e\left(\frac{5}{231}\right)$$ $$e\left(\frac{149}{462}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{3381}(53,\cdot)$$ 3381.ci 462 yes $$1$$ $$1$$ $$e\left(\frac{193}{462}\right)$$ $$e\left(\frac{193}{231}\right)$$ $$e\left(\frac{62}{231}\right)$$ $$e\left(\frac{39}{154}\right)$$ $$e\left(\frac{317}{462}\right)$$ $$e\left(\frac{184}{231}\right)$$ $$e\left(\frac{73}{77}\right)$$ $$e\left(\frac{155}{231}\right)$$ $$e\left(\frac{115}{231}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{3381}(55,\cdot)$$ 3381.cc 154 no $$-1$$ $$1$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{19}{77}\right)$$ $$e\left(\frac{15}{154}\right)$$ $$e\left(\frac{67}{77}\right)$$ $$e\left(\frac{111}{154}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{89}{154}\right)$$ $$e\left(\frac{38}{77}\right)$$ $$e\left(\frac{39}{154}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{3381}(58,\cdot)$$ 3381.ce 231 no $$1$$ $$1$$ $$e\left(\frac{13}{231}\right)$$ $$e\left(\frac{26}{231}\right)$$ $$e\left(\frac{67}{231}\right)$$ $$e\left(\frac{13}{77}\right)$$ $$e\left(\frac{80}{231}\right)$$ $$e\left(\frac{20}{231}\right)$$ $$e\left(\frac{23}{77}\right)$$ $$e\left(\frac{52}{231}\right)$$ $$e\left(\frac{128}{231}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{3381}(59,\cdot)$$ 3381.cj 462 yes $$1$$ $$1$$ $$e\left(\frac{379}{462}\right)$$ $$e\left(\frac{148}{231}\right)$$ $$e\left(\frac{26}{231}\right)$$ $$e\left(\frac{71}{154}\right)$$ $$e\left(\frac{431}{462}\right)$$ $$e\left(\frac{281}{462}\right)$$ $$e\left(\frac{19}{154}\right)$$ $$e\left(\frac{65}{231}\right)$$ $$e\left(\frac{160}{231}\right)$$ $$e\left(\frac{25}{66}\right)$$