# Properties

 Modulus $3520$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{80}$$ Order $1280$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3520)

pari: g = idealstar(,3520,2)

## Character group

 sage: G.order()  pari: g.no Order = 1280 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{80}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3520}(2751,\cdot)$, $\chi_{3520}(1541,\cdot)$, $\chi_{3520}(2817,\cdot)$, $\chi_{3520}(321,\cdot)$

## First 32 of 1280 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$29$$
$$\chi_{3520}(1,\cdot)$$ 3520.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3520}(3,\cdot)$$ 3520.ez 80 yes $$1$$ $$1$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{13}{80}\right)$$
$$\chi_{3520}(7,\cdot)$$ 3520.ex 40 no $$-1$$ $$1$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$
$$\chi_{3520}(9,\cdot)$$ 3520.em 40 no $$1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$
$$\chi_{3520}(13,\cdot)$$ 3520.fm 80 yes $$1$$ $$1$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{41}{80}\right)$$
$$\chi_{3520}(17,\cdot)$$ 3520.dm 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{3520}(19,\cdot)$$ 3520.fe 80 yes $$1$$ $$1$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{73}{80}\right)$$
$$\chi_{3520}(21,\cdot)$$ 3520.cy 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{3520}(23,\cdot)$$ 3520.cd 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{3520}(27,\cdot)$$ 3520.ez 80 yes $$1$$ $$1$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{39}{80}\right)$$
$$\chi_{3520}(29,\cdot)$$ 3520.fg 80 yes $$-1$$ $$1$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{37}{80}\right)$$
$$\chi_{3520}(31,\cdot)$$ 3520.ck 10 no $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{3520}(37,\cdot)$$ 3520.fa 80 yes $$-1$$ $$1$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$
$$\chi_{3520}(39,\cdot)$$ 3520.et 40 no $$1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{3520}(41,\cdot)$$ 3520.en 40 no $$-1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$
$$\chi_{3520}(43,\cdot)$$ 3520.dj 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{3520}(47,\cdot)$$ 3520.ef 20 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{3520}(49,\cdot)$$ 3520.dr 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{3520}(51,\cdot)$$ 3520.fd 80 no $$1$$ $$1$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$
$$\chi_{3520}(53,\cdot)$$ 3520.fn 80 yes $$-1$$ $$1$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{11}{80}\right)$$
$$\chi_{3520}(57,\cdot)$$ 3520.ei 40 no $$1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{3520}(59,\cdot)$$ 3520.fc 80 yes $$-1$$ $$1$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$
$$\chi_{3520}(61,\cdot)$$ 3520.fj 80 no $$-1$$ $$1$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{29}{80}\right)$$
$$\chi_{3520}(63,\cdot)$$ 3520.dx 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{3520}(67,\cdot)$$ 3520.cx 16 no $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{3520}(69,\cdot)$$ 3520.fi 80 yes $$1$$ $$1$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{23}{80}\right)$$
$$\chi_{3520}(71,\cdot)$$ 3520.es 40 no $$-1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{3520}(73,\cdot)$$ 3520.ei 40 no $$1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{3520}(79,\cdot)$$ 3520.do 20 no $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{3520}(81,\cdot)$$ 3520.ea 20 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{3520}(83,\cdot)$$ 3520.fl 80 yes $$-1$$ $$1$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$
$$\chi_{3520}(87,\cdot)$$ 3520.cb 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$