Properties

 Modulus $2760$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{44}$$ Order $704$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2760)

pari: g = idealstar(,2760,2)

Character group

 sage: G.order()  pari: g.no Order = 704 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{44}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2760}(2071,\cdot)$, $\chi_{2760}(1381,\cdot)$, $\chi_{2760}(1841,\cdot)$, $\chi_{2760}(1657,\cdot)$, $\chi_{2760}(1201,\cdot)$

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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{2760}(1,\cdot)$$ 2760.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2760}(7,\cdot)$$ 2760.dj 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$
$$\chi_{2760}(11,\cdot)$$ 2760.ca 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{2760}(13,\cdot)$$ 2760.dk 44 no $$-1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$
$$\chi_{2760}(17,\cdot)$$ 2760.dc 44 no $$-1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$
$$\chi_{2760}(19,\cdot)$$ 2760.cv 22 no $$1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{2760}(29,\cdot)$$ 2760.cm 22 yes $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{2760}(31,\cdot)$$ 2760.cu 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{2760}(37,\cdot)$$ 2760.dg 44 no $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$
$$\chi_{2760}(41,\cdot)$$ 2760.ch 22 no $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2760}(43,\cdot)$$ 2760.dl 44 no $$-1$$ $$1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$
$$\chi_{2760}(47,\cdot)$$ 2760.bu 4 no $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$i$$
$$\chi_{2760}(49,\cdot)$$ 2760.cs 22 no $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{2760}(53,\cdot)$$ 2760.dq 44 yes $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$
$$\chi_{2760}(59,\cdot)$$ 2760.ce 22 yes $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{2760}(61,\cdot)$$ 2760.ct 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{2760}(67,\cdot)$$ 2760.dl 44 no $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$
$$\chi_{2760}(71,\cdot)$$ 2760.cp 22 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{2760}(73,\cdot)$$ 2760.di 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$
$$\chi_{2760}(77,\cdot)$$ 2760.de 44 yes $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$
$$\chi_{2760}(79,\cdot)$$ 2760.cq 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{2760}(83,\cdot)$$ 2760.df 44 yes $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$
$$\chi_{2760}(89,\cdot)$$ 2760.cd 22 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{2760}(91,\cdot)$$ 2760.r 2 no $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{2760}(97,\cdot)$$ 2760.dm 44 no $$1$$ $$1$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$
$$\chi_{2760}(101,\cdot)$$ 2760.cc 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{2760}(103,\cdot)$$ 2760.dj 44 no $$-1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$
$$\chi_{2760}(107,\cdot)$$ 2760.df 44 yes $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$
$$\chi_{2760}(109,\cdot)$$ 2760.bx 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{2760}(113,\cdot)$$ 2760.dc 44 no $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{2760}(119,\cdot)$$ 2760.cb 22 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{2760}(121,\cdot)$$ 2760.bw 11 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
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