# Properties

 Modulus $1840$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{44}$$ Order $704$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1840)

pari: g = idealstar(,1840,2)

## Character group

 sage: G.order()  pari: g.no Order = 704 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{44}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1840}(1151,\cdot)$, $\chi_{1840}(1381,\cdot)$, $\chi_{1840}(737,\cdot)$, $\chi_{1840}(1201,\cdot)$

## First 32 of 704 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$
$$\chi_{1840}(1,\cdot)$$ 1840.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1840}(3,\cdot)$$ 1840.ch 44 yes $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$
$$\chi_{1840}(7,\cdot)$$ 1840.cq 44 no $$-1$$ $$1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{1840}(9,\cdot)$$ 1840.bv 22 no $$1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{1840}(11,\cdot)$$ 1840.cw 44 no $$1$$ $$1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$
$$\chi_{1840}(13,\cdot)$$ 1840.db 44 yes $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{1840}(17,\cdot)$$ 1840.ct 44 no $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{1840}(19,\cdot)$$ 1840.cj 44 yes $$1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{1840}(21,\cdot)$$ 1840.cl 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$
$$\chi_{1840}(27,\cdot)$$ 1840.ch 44 yes $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{1840}(29,\cdot)$$ 1840.ck 44 yes $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$
$$\chi_{1840}(31,\cdot)$$ 1840.cc 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{1840}(33,\cdot)$$ 1840.ct 44 no $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{1840}(37,\cdot)$$ 1840.da 44 yes $$1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$
$$\chi_{1840}(39,\cdot)$$ 1840.bx 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{1840}(41,\cdot)$$ 1840.bz 22 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{1840}(43,\cdot)$$ 1840.cz 44 yes $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$
$$\chi_{1840}(47,\cdot)$$ 1840.ba 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{1840}(49,\cdot)$$ 1840.ca 22 no $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{1840}(51,\cdot)$$ 1840.cw 44 no $$1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$
$$\chi_{1840}(53,\cdot)$$ 1840.cf 44 yes $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$
$$\chi_{1840}(57,\cdot)$$ 1840.cm 44 no $$1$$ $$1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{1840}(59,\cdot)$$ 1840.cx 44 yes $$-1$$ $$1$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{1840}(61,\cdot)$$ 1840.cl 44 no $$-1$$ $$1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$
$$\chi_{1840}(63,\cdot)$$ 1840.cp 44 no $$-1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{1840}(67,\cdot)$$ 1840.cz 44 yes $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$
$$\chi_{1840}(71,\cdot)$$ 1840.bt 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1840}(73,\cdot)$$ 1840.cs 44 no $$-1$$ $$1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{1840}(77,\cdot)$$ 1840.ce 44 yes $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$
$$\chi_{1840}(79,\cdot)$$ 1840.bs 22 no $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{1840}(81,\cdot)$$ 1840.bo 11 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{1840}(83,\cdot)$$ 1840.cg 44 yes $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$