# Properties

 Modulus $1441$ Structure $$C_{130}\times C_{10}$$ Order $1300$

# Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1441)

pari: g = idealstar(,1441,2)

## Character group

 sage: G.order()  pari: g.no Order = 1300 sage: H.invariants()  pari: g.cyc Structure = $$C_{130}\times C_{10}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1441}(1311,\cdot)$, $\chi_{1441}(133,\cdot)$

## First 32 of 1300 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{1441}(1,\cdot)$$ 1441.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1441}(2,\cdot)$$ 1441.by 130 yes $$1$$ $$1$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{57}{130}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$
$$\chi_{1441}(3,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$
$$\chi_{1441}(4,\cdot)$$ 1441.bi 65 yes $$1$$ $$1$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$
$$\chi_{1441}(5,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$
$$\chi_{1441}(6,\cdot)$$ 1441.bm 130 yes $$1$$ $$1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$
$$\chi_{1441}(7,\cdot)$$ 1441.bn 130 yes $$-1$$ $$1$$ $$e\left(\frac{57}{130}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{103}{130}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{42}{65}\right)$$
$$\chi_{1441}(8,\cdot)$$ 1441.by 130 yes $$1$$ $$1$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$
$$\chi_{1441}(9,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$
$$\chi_{1441}(10,\cdot)$$ 1441.ca 130 yes $$1$$ $$1$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$
$$\chi_{1441}(12,\cdot)$$ 1441.bl 65 no $$1$$ $$1$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$
$$\chi_{1441}(13,\cdot)$$ 1441.bn 130 yes $$-1$$ $$1$$ $$e\left(\frac{31}{130}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{130}\right)$$ $$e\left(\frac{129}{130}\right)$$ $$e\left(\frac{93}{130}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{1}{130}\right)$$ $$e\left(\frac{16}{65}\right)$$
$$\chi_{1441}(14,\cdot)$$ 1441.bp 130 yes $$-1$$ $$1$$ $$e\left(\frac{71}{130}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{9}{130}\right)$$ $$e\left(\frac{14}{65}\right)$$
$$\chi_{1441}(15,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$
$$\chi_{1441}(16,\cdot)$$ 1441.bi 65 yes $$1$$ $$1$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$
$$\chi_{1441}(17,\cdot)$$ 1441.bm 130 yes $$1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{7}{130}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$
$$\chi_{1441}(18,\cdot)$$ 1441.bz 130 yes $$1$$ $$1$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{127}{130}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{1441}(19,\cdot)$$ 1441.bz 130 yes $$1$$ $$1$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{123}{130}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{1441}(20,\cdot)$$ 1441.bh 65 yes $$1$$ $$1$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$
$$\chi_{1441}(21,\cdot)$$ 1441.bq 130 yes $$-1$$ $$1$$ $$e\left(\frac{103}{130}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{109}{130}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{49}{130}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{31}{130}\right)$$ $$e\left(\frac{41}{65}\right)$$
$$\chi_{1441}(23,\cdot)$$ 1441.bs 130 no $$-1$$ $$1$$ $$e\left(\frac{23}{130}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{69}{130}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{41}{130}\right)$$ $$e\left(\frac{6}{65}\right)$$
$$\chi_{1441}(24,\cdot)$$ 1441.bz 130 yes $$1$$ $$1$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{11}{130}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{1441}(25,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$
$$\chi_{1441}(26,\cdot)$$ 1441.cd 130 yes $$-1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{113}{130}\right)$$ $$e\left(\frac{53}{65}\right)$$
$$\chi_{1441}(27,\cdot)$$ 1441.bj 65 yes $$1$$ $$1$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$
$$\chi_{1441}(28,\cdot)$$ 1441.cc 130 yes $$-1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{17}{130}\right)$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{121}{130}\right)$$ $$e\left(\frac{51}{65}\right)$$
$$\chi_{1441}(29,\cdot)$$ 1441.bx 130 yes $$1$$ $$1$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$
$$\chi_{1441}(30,\cdot)$$ 1441.bx 130 yes $$1$$ $$1$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{127}{130}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$
$$\chi_{1441}(31,\cdot)$$ 1441.bp 130 yes $$-1$$ $$1$$ $$e\left(\frac{107}{130}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{89}{130}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{63}{130}\right)$$ $$e\left(\frac{33}{65}\right)$$
$$\chi_{1441}(32,\cdot)$$ 1441.bd 26 yes $$1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{1441}(34,\cdot)$$ 1441.bl 65 no $$1$$ $$1$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$
$$\chi_{1441}(35,\cdot)$$ 1441.cc 130 yes $$-1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{109}{130}\right)$$ $$e\left(\frac{54}{65}\right)$$