# Properties

 Modulus 8005 Structure $$C_{1600}\times C_{4}$$ Order 6400

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(8005)

pari: g = idealstar(,8005,2)

## Character group

 sage: G.order()  pari: g.no Order = 6400 sage: H.invariants()  pari: g.cyc Structure = $$C_{1600}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8005}(4806,\cdot)$, $\chi_{8005}(1602,\cdot)$

## First 32 of 6400 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.

orbit label order primitive -1 1 2 3 4 6 7 8 9 11 12 13
$$\chi_{8005}(1,\cdot)$$ 8005.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8005}(2,\cdot)$$ 8005.cr 400 yes $$-1$$ $$1$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{313}{400}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{289}{400}\right)$$ $$e\left(\frac{131}{400}\right)$$ $$e\left(\frac{41}{50}\right)$$ $$e\left(\frac{113}{200}\right)$$ $$e\left(\frac{229}{400}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{8005}(3,\cdot)$$ 8005.cy 1600 yes $$1$$ $$1$$ $$e\left(\frac{313}{400}\right)$$ $$e\left(\frac{401}{1600}\right)$$ $$e\left(\frac{113}{200}\right)$$ $$e\left(\frac{53}{1600}\right)$$ $$e\left(\frac{187}{1600}\right)$$ $$e\left(\frac{139}{400}\right)$$ $$e\left(\frac{401}{800}\right)$$ $$e\left(\frac{633}{1600}\right)$$ $$e\left(\frac{261}{320}\right)$$ $$e\left(\frac{25}{64}\right)$$
$$\chi_{8005}(4,\cdot)$$ 8005.cg 200 yes $$1$$ $$1$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{113}{200}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{89}{200}\right)$$ $$e\left(\frac{131}{200}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{13}{100}\right)$$ $$e\left(\frac{29}{200}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{8005}(6,\cdot)$$ 8005.cw 1600 no $$-1$$ $$1$$ $$e\left(\frac{289}{400}\right)$$ $$e\left(\frac{53}{1600}\right)$$ $$e\left(\frac{89}{200}\right)$$ $$e\left(\frac{1209}{1600}\right)$$ $$e\left(\frac{711}{1600}\right)$$ $$e\left(\frac{67}{400}\right)$$ $$e\left(\frac{53}{800}\right)$$ $$e\left(\frac{1549}{1600}\right)$$ $$e\left(\frac{153}{320}\right)$$ $$e\left(\frac{29}{64}\right)$$
$$\chi_{8005}(7,\cdot)$$ 8005.cy 1600 yes $$1$$ $$1$$ $$e\left(\frac{131}{400}\right)$$ $$e\left(\frac{187}{1600}\right)$$ $$e\left(\frac{131}{200}\right)$$ $$e\left(\frac{711}{1600}\right)$$ $$e\left(\frac{969}{1600}\right)$$ $$e\left(\frac{393}{400}\right)$$ $$e\left(\frac{187}{800}\right)$$ $$e\left(\frac{371}{1600}\right)$$ $$e\left(\frac{247}{320}\right)$$ $$e\left(\frac{19}{64}\right)$$
$$\chi_{8005}(8,\cdot)$$ 8005.cr 400 yes $$-1$$ $$1$$ $$e\left(\frac{41}{50}\right)$$ $$e\left(\frac{139}{400}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{67}{400}\right)$$ $$e\left(\frac{393}{400}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{287}{400}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{8005}(9,\cdot)$$ 8005.cv 800 yes $$1$$ $$1$$ $$e\left(\frac{113}{200}\right)$$ $$e\left(\frac{401}{800}\right)$$ $$e\left(\frac{13}{100}\right)$$ $$e\left(\frac{53}{800}\right)$$ $$e\left(\frac{187}{800}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{1}{400}\right)$$ $$e\left(\frac{633}{800}\right)$$ $$e\left(\frac{101}{160}\right)$$ $$e\left(\frac{25}{32}\right)$$
$$\chi_{8005}(11,\cdot)$$ 8005.cw 1600 no $$-1$$ $$1$$ $$e\left(\frac{229}{400}\right)$$ $$e\left(\frac{633}{1600}\right)$$ $$e\left(\frac{29}{200}\right)$$ $$e\left(\frac{1549}{1600}\right)$$ $$e\left(\frac{371}{1600}\right)$$ $$e\left(\frac{287}{400}\right)$$ $$e\left(\frac{633}{800}\right)$$ $$e\left(\frac{689}{1600}\right)$$ $$e\left(\frac{173}{320}\right)$$ $$e\left(\frac{1}{64}\right)$$
$$\chi_{8005}(12,\cdot)$$ 8005.cm 320 yes $$1$$ $$1$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{261}{320}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{153}{320}\right)$$ $$e\left(\frac{247}{320}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{101}{160}\right)$$ $$e\left(\frac{173}{320}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{33}{64}\right)$$
$$\chi_{8005}(13,\cdot)$$ 8005.bo 64 yes $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$
$$\chi_{8005}(14,\cdot)$$ 8005.cz 1600 yes $$-1$$ $$1$$ $$e\left(\frac{107}{400}\right)$$ $$e\left(\frac{1439}{1600}\right)$$ $$e\left(\frac{107}{200}\right)$$ $$e\left(\frac{267}{1600}\right)$$ $$e\left(\frac{1493}{1600}\right)$$ $$e\left(\frac{321}{400}\right)$$ $$e\left(\frac{639}{800}\right)$$ $$e\left(\frac{1287}{1600}\right)$$ $$e\left(\frac{139}{320}\right)$$ $$e\left(\frac{23}{64}\right)$$
$$\chi_{8005}(16,\cdot)$$ 8005.bx 100 no $$1$$ $$1$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{13}{100}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{29}{100}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$
$$\chi_{8005}(17,\cdot)$$ 8005.cy 1600 yes $$1$$ $$1$$ $$e\left(\frac{259}{400}\right)$$ $$e\left(\frac{1243}{1600}\right)$$ $$e\left(\frac{59}{200}\right)$$ $$e\left(\frac{679}{1600}\right)$$ $$e\left(\frac{41}{1600}\right)$$ $$e\left(\frac{377}{400}\right)$$ $$e\left(\frac{443}{800}\right)$$ $$e\left(\frac{19}{1600}\right)$$ $$e\left(\frac{23}{320}\right)$$ $$e\left(\frac{51}{64}\right)$$
$$\chi_{8005}(18,\cdot)$$ 8005.ct 800 yes $$-1$$ $$1$$ $$e\left(\frac{101}{200}\right)$$ $$e\left(\frac{227}{800}\right)$$ $$e\left(\frac{1}{100}\right)$$ $$e\left(\frac{631}{800}\right)$$ $$e\left(\frac{449}{800}\right)$$ $$e\left(\frac{103}{200}\right)$$ $$e\left(\frac{227}{400}\right)$$ $$e\left(\frac{291}{800}\right)$$ $$e\left(\frac{47}{160}\right)$$ $$e\left(\frac{27}{32}\right)$$
$$\chi_{8005}(19,\cdot)$$ 8005.bn 50 yes $$1$$ $$1$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{41}{50}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$
$$\chi_{8005}(21,\cdot)$$ 8005.cp 400 no $$1$$ $$1$$ $$e\left(\frac{11}{100}\right)$$ $$e\left(\frac{147}{400}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{191}{400}\right)$$ $$e\left(\frac{289}{400}\right)$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{147}{200}\right)$$ $$e\left(\frac{251}{400}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{8005}(22,\cdot)$$ 8005.cm 320 yes $$1$$ $$1$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{57}{320}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{221}{320}\right)$$ $$e\left(\frac{179}{320}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{57}{160}\right)$$ $$e\left(\frac{1}{320}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{5}{64}\right)$$
$$\chi_{8005}(23,\cdot)$$ 8005.cx 1600 yes $$1$$ $$1$$ $$e\left(\frac{47}{400}\right)$$ $$e\left(\frac{319}{1600}\right)$$ $$e\left(\frac{47}{200}\right)$$ $$e\left(\frac{507}{1600}\right)$$ $$e\left(\frac{53}{1600}\right)$$ $$e\left(\frac{141}{400}\right)$$ $$e\left(\frac{319}{800}\right)$$ $$e\left(\frac{1527}{1600}\right)$$ $$e\left(\frac{139}{320}\right)$$ $$e\left(\frac{55}{64}\right)$$
$$\chi_{8005}(24,\cdot)$$ 8005.cz 1600 yes $$-1$$ $$1$$ $$e\left(\frac{241}{400}\right)$$ $$e\left(\frac{957}{1600}\right)$$ $$e\left(\frac{41}{200}\right)$$ $$e\left(\frac{321}{1600}\right)$$ $$e\left(\frac{159}{1600}\right)$$ $$e\left(\frac{323}{400}\right)$$ $$e\left(\frac{157}{800}\right)$$ $$e\left(\frac{181}{1600}\right)$$ $$e\left(\frac{257}{320}\right)$$ $$e\left(\frac{37}{64}\right)$$
$$\chi_{8005}(26,\cdot)$$ 8005.cw 1600 no $$-1$$ $$1$$ $$e\left(\frac{1}{400}\right)$$ $$e\left(\frac{277}{1600}\right)$$ $$e\left(\frac{1}{200}\right)$$ $$e\left(\frac{281}{1600}\right)$$ $$e\left(\frac{999}{1600}\right)$$ $$e\left(\frac{3}{400}\right)$$ $$e\left(\frac{277}{800}\right)$$ $$e\left(\frac{941}{1600}\right)$$ $$e\left(\frac{57}{320}\right)$$ $$e\left(\frac{61}{64}\right)$$
$$\chi_{8005}(27,\cdot)$$ 8005.cy 1600 yes $$1$$ $$1$$ $$e\left(\frac{139}{400}\right)$$ $$e\left(\frac{1203}{1600}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{159}{1600}\right)$$ $$e\left(\frac{561}{1600}\right)$$ $$e\left(\frac{17}{400}\right)$$ $$e\left(\frac{403}{800}\right)$$ $$e\left(\frac{299}{1600}\right)$$ $$e\left(\frac{143}{320}\right)$$ $$e\left(\frac{11}{64}\right)$$
$$\chi_{8005}(28,\cdot)$$ 8005.cx 1600 yes $$1$$ $$1$$ $$e\left(\frac{83}{400}\right)$$ $$e\left(\frac{1091}{1600}\right)$$ $$e\left(\frac{83}{200}\right)$$ $$e\left(\frac{1423}{1600}\right)$$ $$e\left(\frac{417}{1600}\right)$$ $$e\left(\frac{249}{400}\right)$$ $$e\left(\frac{291}{800}\right)$$ $$e\left(\frac{603}{1600}\right)$$ $$e\left(\frac{31}{320}\right)$$ $$e\left(\frac{27}{64}\right)$$
$$\chi_{8005}(29,\cdot)$$ 8005.cg 200 yes $$1$$ $$1$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{197}{200}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{141}{200}\right)$$ $$e\left(\frac{39}{200}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{97}{100}\right)$$ $$e\left(\frac{1}{200}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{8005}(31,\cdot)$$ 8005.bx 100 no $$1$$ $$1$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{19}{100}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{7}{100}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$
$$\chi_{8005}(32,\cdot)$$ 8005.bv 80 yes $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{8005}(33,\cdot)$$ 8005.cu 800 yes $$-1$$ $$1$$ $$e\left(\frac{71}{200}\right)$$ $$e\left(\frac{517}{800}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{1}{800}\right)$$ $$e\left(\frac{279}{800}\right)$$ $$e\left(\frac{13}{200}\right)$$ $$e\left(\frac{117}{400}\right)$$ $$e\left(\frac{661}{800}\right)$$ $$e\left(\frac{57}{160}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{8005}(34,\cdot)$$ 8005.ck 320 yes $$-1$$ $$1$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{179}{320}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{47}{320}\right)$$ $$e\left(\frac{113}{320}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{19}{160}\right)$$ $$e\left(\frac{187}{320}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$
$$\chi_{8005}(36,\cdot)$$ 8005.cs 800 no $$1$$ $$1$$ $$e\left(\frac{89}{200}\right)$$ $$e\left(\frac{53}{800}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{409}{800}\right)$$ $$e\left(\frac{711}{800}\right)$$ $$e\left(\frac{67}{200}\right)$$ $$e\left(\frac{53}{400}\right)$$ $$e\left(\frac{749}{800}\right)$$ $$e\left(\frac{153}{160}\right)$$ $$e\left(\frac{29}{32}\right)$$
$$\chi_{8005}(37,\cdot)$$ 8005.ct 800 yes $$-1$$ $$1$$ $$e\left(\frac{79}{200}\right)$$ $$e\left(\frac{233}{800}\right)$$ $$e\left(\frac{79}{100}\right)$$ $$e\left(\frac{549}{800}\right)$$ $$e\left(\frac{771}{800}\right)$$ $$e\left(\frac{37}{200}\right)$$ $$e\left(\frac{233}{400}\right)$$ $$e\left(\frac{489}{800}\right)$$ $$e\left(\frac{13}{160}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{8005}(38,\cdot)$$ 8005.co 400 yes $$-1$$ $$1$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{1}{400}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{353}{400}\right)$$ $$e\left(\frac{187}{400}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{1}{200}\right)$$ $$e\left(\frac{133}{400}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{8005}(39,\cdot)$$ 8005.cv 800 yes $$1$$ $$1$$ $$e\left(\frac{169}{200}\right)$$ $$e\left(\frac{513}{800}\right)$$ $$e\left(\frac{69}{100}\right)$$ $$e\left(\frac{389}{800}\right)$$ $$e\left(\frac{331}{800}\right)$$ $$e\left(\frac{107}{200}\right)$$ $$e\left(\frac{113}{400}\right)$$ $$e\left(\frac{329}{800}\right)$$ $$e\left(\frac{53}{160}\right)$$ $$e\left(\frac{9}{32}\right)$$