# Properties

 Modulus $1600$ Structure $$C_{2}\times C_{4}\times C_{80}$$ Order $640$

# Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1600)

pari: g = idealstar(,1600,2)

## Character group

 sage: G.order()  pari: g.no Order = 640 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}\times C_{80}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1600}(1151,\cdot)$, $\chi_{1600}(901,\cdot)$, $\chi_{1600}(577,\cdot)$

## First 32 of 640 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{1600}(1,\cdot)$$ 1600.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1600}(3,\cdot)$$ 1600.cm 80 yes $$1$$ $$1$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{43}{80}\right)$$
$$\chi_{1600}(7,\cdot)$$ 1600.bb 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{1600}(9,\cdot)$$ 1600.cg 40 no $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{1600}(11,\cdot)$$ 1600.cp 80 yes $$-1$$ $$1$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{9}{80}\right)$$
$$\chi_{1600}(13,\cdot)$$ 1600.cn 80 yes $$-1$$ $$1$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{31}{80}\right)$$
$$\chi_{1600}(17,\cdot)$$ 1600.bs 20 no $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1600}(19,\cdot)$$ 1600.co 80 yes $$-1$$ $$1$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{27}{80}\right)$$
$$\chi_{1600}(21,\cdot)$$ 1600.cr 80 yes $$1$$ $$1$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{73}{80}\right)$$
$$\chi_{1600}(23,\cdot)$$ 1600.cl 40 no $$1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{1600}(27,\cdot)$$ 1600.cm 80 yes $$1$$ $$1$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{49}{80}\right)$$
$$\chi_{1600}(29,\cdot)$$ 1600.cq 80 yes $$1$$ $$1$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{23}{80}\right)$$
$$\chi_{1600}(31,\cdot)$$ 1600.bd 10 no $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1600}(33,\cdot)$$ 1600.bz 20 no $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{1600}(37,\cdot)$$ 1600.cn 80 yes $$-1$$ $$1$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{41}{80}\right)$$
$$\chi_{1600}(39,\cdot)$$ 1600.ch 40 no $$-1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{1600}(41,\cdot)$$ 1600.ci 40 no $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$-i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{1600}(43,\cdot)$$ 1600.bl 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{1600}(47,\cdot)$$ 1600.cc 20 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1600}(49,\cdot)$$ 1600.q 4 no $$1$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$-i$$
$$\chi_{1600}(51,\cdot)$$ 1600.bo 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1600}(53,\cdot)$$ 1600.ct 80 yes $$-1$$ $$1$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{13}{80}\right)$$
$$\chi_{1600}(57,\cdot)$$ 1600.w 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1600}(59,\cdot)$$ 1600.co 80 yes $$-1$$ $$1$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{61}{80}\right)$$
$$\chi_{1600}(61,\cdot)$$ 1600.cr 80 yes $$1$$ $$1$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{39}{80}\right)$$
$$\chi_{1600}(63,\cdot)$$ 1600.by 20 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{1600}(67,\cdot)$$ 1600.cs 80 yes $$1$$ $$1$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{67}{80}\right)$$
$$\chi_{1600}(69,\cdot)$$ 1600.cq 80 yes $$1$$ $$1$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{37}{80}\right)$$
$$\chi_{1600}(71,\cdot)$$ 1600.cj 40 no $$-1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$-i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$
$$\chi_{1600}(73,\cdot)$$ 1600.ce 40 no $$-1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$-1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{1600}(77,\cdot)$$ 1600.ct 80 yes $$-1$$ $$1$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{39}{80}\right)$$
$$\chi_{1600}(79,\cdot)$$ 1600.bv 20 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$
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