# Properties

 Modulus 8041 Structure $$C_{1680}\times C_{2}\times C_{2}$$ Order 6720

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(8041)

pari: g = idealstar(,8041,2)

## Character group

 sage: G.order()  pari: g.no Order = 6720 sage: H.invariants()  pari: g.cyc Structure = $$C_{1680}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8041}(3185,\cdot)$, $\chi_{8041}(8040,\cdot)$, $\chi_{8041}(7481,\cdot)$

## First 32 of 6720 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 5 6 7 8 9 10 12
$$\chi_{8041}(1,\cdot)$$ 8041.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8041}(2,\cdot)$$ 8041.fj 280 yes $$1$$ $$1$$ $$e\left(\frac{99}{140}\right)$$ $$e\left(\frac{89}{280}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{237}{280}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{140}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{41}{56}\right)$$
$$\chi_{8041}(3,\cdot)$$ 8041.gd 1680 yes $$1$$ $$1$$ $$e\left(\frac{89}{280}\right)$$ $$e\left(\frac{817}{1680}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{181}{1680}\right)$$ $$e\left(\frac{193}{240}\right)$$ $$e\left(\frac{29}{240}\right)$$ $$e\left(\frac{267}{280}\right)$$ $$e\left(\frac{817}{840}\right)$$ $$e\left(\frac{143}{336}\right)$$ $$e\left(\frac{41}{336}\right)$$
$$\chi_{8041}(4,\cdot)$$ 8041.eo 140 yes $$1$$ $$1$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{97}{140}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{8041}(5,\cdot)$$ 8041.gd 1680 yes $$1$$ $$1$$ $$e\left(\frac{237}{280}\right)$$ $$e\left(\frac{181}{1680}\right)$$ $$e\left(\frac{97}{140}\right)$$ $$e\left(\frac{73}{1680}\right)$$ $$e\left(\frac{229}{240}\right)$$ $$e\left(\frac{17}{240}\right)$$ $$e\left(\frac{151}{280}\right)$$ $$e\left(\frac{181}{840}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{269}{336}\right)$$
$$\chi_{8041}(6,\cdot)$$ 8041.fd 240 yes $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{193}{240}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{229}{240}\right)$$ $$e\left(\frac{199}{240}\right)$$ $$e\left(\frac{227}{240}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$
$$\chi_{8041}(7,\cdot)$$ 8041.ff 240 yes $$-1$$ $$1$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{29}{240}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{240}\right)$$ $$e\left(\frac{227}{240}\right)$$ $$e\left(\frac{151}{240}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{8041}(8,\cdot)$$ 8041.fj 280 yes $$1$$ $$1$$ $$e\left(\frac{17}{140}\right)$$ $$e\left(\frac{267}{280}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{151}{280}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{51}{140}\right)$$ $$e\left(\frac{127}{140}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{11}{56}\right)$$
$$\chi_{8041}(9,\cdot)$$ 8041.fy 840 yes $$1$$ $$1$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{817}{840}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{181}{840}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{127}{140}\right)$$ $$e\left(\frac{397}{420}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{41}{168}\right)$$
$$\chi_{8041}(10,\cdot)$$ 8041.fl 336 yes $$1$$ $$1$$ $$e\left(\frac{31}{56}\right)$$ $$e\left(\frac{143}{336}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{149}{336}\right)$$ $$e\left(\frac{179}{336}\right)$$
$$\chi_{8041}(12,\cdot)$$ 8041.fk 336 no $$1$$ $$1$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{41}{336}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{269}{336}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{56}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{179}{336}\right)$$ $$e\left(\frac{197}{336}\right)$$
$$\chi_{8041}(13,\cdot)$$ 8041.fr 420 yes $$-1$$ $$1$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{341}{420}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{293}{420}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{13}{84}\right)$$
$$\chi_{8041}(14,\cdot)$$ 8041.gb 1680 yes $$-1$$ $$1$$ $$e\left(\frac{149}{280}\right)$$ $$e\left(\frac{737}{1680}\right)$$ $$e\left(\frac{9}{140}\right)$$ $$e\left(\frac{1541}{1680}\right)$$ $$e\left(\frac{233}{240}\right)$$ $$e\left(\frac{109}{240}\right)$$ $$e\left(\frac{167}{280}\right)$$ $$e\left(\frac{737}{840}\right)$$ $$e\left(\frac{151}{336}\right)$$ $$e\left(\frac{169}{336}\right)$$
$$\chi_{8041}(15,\cdot)$$ 8041.fy 840 yes $$1$$ $$1$$ $$e\left(\frac{23}{140}\right)$$ $$e\left(\frac{499}{840}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{127}{840}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{69}{140}\right)$$ $$e\left(\frac{79}{420}\right)$$ $$e\left(\frac{53}{168}\right)$$ $$e\left(\frac{155}{168}\right)$$
$$\chi_{8041}(16,\cdot)$$ 8041.du 70 yes $$1$$ $$1$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{8041}(18,\cdot)$$ 8041.fb 210 no $$1$$ $$1$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{61}{210}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{13}{210}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{61}{105}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$
$$\chi_{8041}(19,\cdot)$$ 8041.fw 840 yes $$1$$ $$1$$ $$e\left(\frac{107}{140}\right)$$ $$e\left(\frac{611}{840}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{743}{840}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{41}{140}\right)$$ $$e\left(\frac{191}{420}\right)$$ $$e\left(\frac{109}{168}\right)$$ $$e\left(\frac{43}{168}\right)$$
$$\chi_{8041}(20,\cdot)$$ 8041.gd 1680 yes $$1$$ $$1$$ $$e\left(\frac{73}{280}\right)$$ $$e\left(\frac{1249}{1680}\right)$$ $$e\left(\frac{73}{140}\right)$$ $$e\left(\frac{1237}{1680}\right)$$ $$e\left(\frac{1}{240}\right)$$ $$e\left(\frac{173}{240}\right)$$ $$e\left(\frac{219}{280}\right)$$ $$e\left(\frac{409}{840}\right)$$ $$e\left(\frac{335}{336}\right)$$ $$e\left(\frac{89}{336}\right)$$
$$\chi_{8041}(21,\cdot)$$ 8041.ch 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$
$$\chi_{8041}(23,\cdot)$$ 8041.fm 336 no $$-1$$ $$1$$ $$e\left(\frac{23}{56}\right)$$ $$e\left(\frac{107}{336}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{71}{336}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{107}{168}\right)$$ $$e\left(\frac{209}{336}\right)$$ $$e\left(\frac{47}{336}\right)$$
$$\chi_{8041}(24,\cdot)$$ 8041.gc 1680 yes $$1$$ $$1$$ $$e\left(\frac{123}{280}\right)$$ $$e\left(\frac{739}{1680}\right)$$ $$e\left(\frac{123}{140}\right)$$ $$e\left(\frac{1087}{1680}\right)$$ $$e\left(\frac{211}{240}\right)$$ $$e\left(\frac{143}{240}\right)$$ $$e\left(\frac{89}{280}\right)$$ $$e\left(\frac{739}{840}\right)$$ $$e\left(\frac{29}{336}\right)$$ $$e\left(\frac{107}{336}\right)$$
$$\chi_{8041}(25,\cdot)$$ 8041.fy 840 yes $$1$$ $$1$$ $$e\left(\frac{97}{140}\right)$$ $$e\left(\frac{181}{840}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{73}{840}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{11}{140}\right)$$ $$e\left(\frac{181}{420}\right)$$ $$e\left(\frac{131}{168}\right)$$ $$e\left(\frac{101}{168}\right)$$
$$\chi_{8041}(26,\cdot)$$ 8041.fz 840 yes $$-1$$ $$1$$ $$e\left(\frac{123}{140}\right)$$ $$e\left(\frac{109}{840}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{457}{840}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{109}{420}\right)$$ $$e\left(\frac{71}{168}\right)$$ $$e\left(\frac{149}{168}\right)$$
$$\chi_{8041}(27,\cdot)$$ 8041.ft 560 yes $$1$$ $$1$$ $$e\left(\frac{267}{280}\right)$$ $$e\left(\frac{257}{560}\right)$$ $$e\left(\frac{127}{140}\right)$$ $$e\left(\frac{181}{560}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{241}{280}\right)$$ $$e\left(\frac{257}{280}\right)$$ $$e\left(\frac{31}{112}\right)$$ $$e\left(\frac{41}{112}\right)$$
$$\chi_{8041}(28,\cdot)$$ 8041.ga 1680 yes $$-1$$ $$1$$ $$e\left(\frac{67}{280}\right)$$ $$e\left(\frac{1271}{1680}\right)$$ $$e\left(\frac{67}{140}\right)$$ $$e\left(\frac{1283}{1680}\right)$$ $$e\left(\frac{239}{240}\right)$$ $$e\left(\frac{67}{240}\right)$$ $$e\left(\frac{201}{280}\right)$$ $$e\left(\frac{431}{840}\right)$$ $$e\left(\frac{1}{336}\right)$$ $$e\left(\frac{79}{336}\right)$$
$$\chi_{8041}(29,\cdot)$$ 8041.ga 1680 yes $$-1$$ $$1$$ $$e\left(\frac{121}{280}\right)$$ $$e\left(\frac{653}{1680}\right)$$ $$e\left(\frac{121}{140}\right)$$ $$e\left(\frac{449}{1680}\right)$$ $$e\left(\frac{197}{240}\right)$$ $$e\left(\frac{1}{240}\right)$$ $$e\left(\frac{83}{280}\right)$$ $$e\left(\frac{653}{840}\right)$$ $$e\left(\frac{235}{336}\right)$$ $$e\left(\frac{85}{336}\right)$$
$$\chi_{8041}(30,\cdot)$$ 8041.fp 420 yes $$1$$ $$1$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{383}{420}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{419}{420}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{43}{70}\right)$$ $$e\left(\frac{173}{210}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{55}{84}\right)$$
$$\chi_{8041}(31,\cdot)$$ 8041.gb 1680 yes $$-1$$ $$1$$ $$e\left(\frac{93}{280}\right)$$ $$e\left(\frac{289}{1680}\right)$$ $$e\left(\frac{93}{140}\right)$$ $$e\left(\frac{757}{1680}\right)$$ $$e\left(\frac{121}{240}\right)$$ $$e\left(\frac{173}{240}\right)$$ $$e\left(\frac{279}{280}\right)$$ $$e\left(\frac{289}{840}\right)$$ $$e\left(\frac{263}{336}\right)$$ $$e\left(\frac{281}{336}\right)$$
$$\chi_{8041}(32,\cdot)$$ 8041.dh 56 yes $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{37}{56}\right)$$
$$\chi_{8041}(35,\cdot)$$ 8041.ds 70 no $$-1$$ $$1$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{8041}(36,\cdot)$$ 8041.ek 120 yes $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{8041}(37,\cdot)$$ 8041.fc 240 yes $$1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{199}{240}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{67}{240}\right)$$ $$e\left(\frac{97}{240}\right)$$ $$e\left(\frac{221}{240}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$