# Properties

 Modulus 7623 Structure $$C_{330}\times C_{6}\times C_{2}$$ Order 3960

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(7623)

pari: g = idealstar(,7623,2)

## Character group

 sage: G.order()  pari: g.no Order = 3960 sage: H.invariants()  pari: g.cyc Structure = $$C_{330}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7623}(5689,\cdot)$, $\chi_{7623}(848,\cdot)$, $\chi_{7623}(6049,\cdot)$

## First 32 of 3960 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 4 5 8 10 13 16 17 19 20
$$\chi_{7623}(1,\cdot)$$ 7623.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7623}(2,\cdot)$$ 7623.fg 330 yes $$1$$ $$1$$ $$e\left(\frac{139}{165}\right)$$ $$e\left(\frac{113}{165}\right)$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{83}{330}\right)$$ $$e\left(\frac{61}{165}\right)$$ $$e\left(\frac{46}{165}\right)$$ $$e\left(\frac{139}{330}\right)$$ $$e\left(\frac{283}{330}\right)$$
$$\chi_{7623}(4,\cdot)$$ 7623.fa 165 yes $$1$$ $$1$$ $$e\left(\frac{113}{165}\right)$$ $$e\left(\frac{61}{165}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{83}{165}\right)$$ $$e\left(\frac{122}{165}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{139}{165}\right)$$ $$e\left(\frac{118}{165}\right)$$
$$\chi_{7623}(5,\cdot)$$ 7623.fc 330 yes $$1$$ $$1$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{19}{165}\right)$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{37}{330}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{49}{165}\right)$$ $$e\left(\frac{1}{330}\right)$$ $$e\left(\frac{76}{165}\right)$$
$$\chi_{7623}(8,\cdot)$$ 7623.ew 110 no $$1$$ $$1$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{83}{110}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{63}{110}\right)$$
$$\chi_{7623}(10,\cdot)$$ 7623.dx 66 no $$1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{7623}(13,\cdot)$$ 7623.fw 330 yes $$1$$ $$1$$ $$e\left(\frac{83}{330}\right)$$ $$e\left(\frac{83}{165}\right)$$ $$e\left(\frac{37}{330}\right)$$ $$e\left(\frac{83}{110}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{149}{165}\right)$$ $$e\left(\frac{1}{165}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{39}{55}\right)$$ $$e\left(\frac{203}{330}\right)$$
$$\chi_{7623}(16,\cdot)$$ 7623.fa 165 yes $$1$$ $$1$$ $$e\left(\frac{61}{165}\right)$$ $$e\left(\frac{122}{165}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{165}\right)$$ $$e\left(\frac{79}{165}\right)$$ $$e\left(\frac{19}{165}\right)$$ $$e\left(\frac{113}{165}\right)$$ $$e\left(\frac{71}{165}\right)$$
$$\chi_{7623}(17,\cdot)$$ 7623.fj 330 no $$-1$$ $$1$$ $$e\left(\frac{46}{165}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{49}{165}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{19}{165}\right)$$ $$e\left(\frac{163}{330}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{47}{55}\right)$$
$$\chi_{7623}(19,\cdot)$$ 7623.fx 330 no $$1$$ $$1$$ $$e\left(\frac{139}{330}\right)$$ $$e\left(\frac{139}{165}\right)$$ $$e\left(\frac{1}{330}\right)$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{39}{55}\right)$$ $$e\left(\frac{113}{165}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{131}{165}\right)$$ $$e\left(\frac{93}{110}\right)$$
$$\chi_{7623}(20,\cdot)$$ 7623.fu 330 yes $$1$$ $$1$$ $$e\left(\frac{283}{330}\right)$$ $$e\left(\frac{118}{165}\right)$$ $$e\left(\frac{76}{165}\right)$$ $$e\left(\frac{63}{110}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{203}{330}\right)$$ $$e\left(\frac{71}{165}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{93}{110}\right)$$ $$e\left(\frac{29}{165}\right)$$
$$\chi_{7623}(23,\cdot)$$ 7623.en 66 yes $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$
$$\chi_{7623}(25,\cdot)$$ 7623.fb 165 yes $$1$$ $$1$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{38}{165}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{37}{165}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{98}{165}\right)$$ $$e\left(\frac{1}{165}\right)$$ $$e\left(\frac{152}{165}\right)$$
$$\chi_{7623}(26,\cdot)$$ 7623.fr 330 no $$1$$ $$1$$ $$e\left(\frac{31}{330}\right)$$ $$e\left(\frac{31}{165}\right)$$ $$e\left(\frac{47}{165}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{17}{110}\right)$$ $$e\left(\frac{62}{165}\right)$$ $$e\left(\frac{127}{165}\right)$$ $$e\left(\frac{43}{330}\right)$$ $$e\left(\frac{26}{55}\right)$$
$$\chi_{7623}(29,\cdot)$$ 7623.fn 330 no $$1$$ $$1$$ $$e\left(\frac{53}{165}\right)$$ $$e\left(\frac{106}{165}\right)$$ $$e\left(\frac{89}{330}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{311}{330}\right)$$ $$e\left(\frac{47}{165}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{301}{330}\right)$$
$$\chi_{7623}(31,\cdot)$$ 7623.fh 330 yes $$-1$$ $$1$$ $$e\left(\frac{74}{165}\right)$$ $$e\left(\frac{148}{165}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{43}{330}\right)$$ $$e\left(\frac{131}{165}\right)$$ $$e\left(\frac{157}{330}\right)$$ $$e\left(\frac{239}{330}\right)$$ $$e\left(\frac{83}{330}\right)$$
$$\chi_{7623}(32,\cdot)$$ 7623.em 66 yes $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{7623}(34,\cdot)$$ 7623.ei 66 yes $$-1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$
$$\chi_{7623}(37,\cdot)$$ 7623.ez 165 no $$1$$ $$1$$ $$e\left(\frac{8}{165}\right)$$ $$e\left(\frac{16}{165}\right)$$ $$e\left(\frac{152}{165}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{32}{165}\right)$$ $$e\left(\frac{7}{165}\right)$$ $$e\left(\frac{59}{165}\right)$$ $$e\left(\frac{1}{55}\right)$$
$$\chi_{7623}(38,\cdot)$$ 7623.fc 330 yes $$1$$ $$1$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{29}{165}\right)$$ $$e\left(\frac{87}{110}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{317}{330}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{14}{165}\right)$$ $$e\left(\frac{71}{330}\right)$$ $$e\left(\frac{116}{165}\right)$$
$$\chi_{7623}(40,\cdot)$$ 7623.dh 30 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{7623}(41,\cdot)$$ 7623.fi 330 yes $$-1$$ $$1$$ $$e\left(\frac{7}{165}\right)$$ $$e\left(\frac{14}{165}\right)$$ $$e\left(\frac{23}{165}\right)$$ $$e\left(\frac{7}{55}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{47}{165}\right)$$ $$e\left(\frac{28}{165}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{37}{165}\right)$$
$$\chi_{7623}(43,\cdot)$$ 7623.eb 66 no $$-1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{7623}(46,\cdot)$$ 7623.fs 330 no $$-1$$ $$1$$ $$e\left(\frac{323}{330}\right)$$ $$e\left(\frac{158}{165}\right)$$ $$e\left(\frac{16}{165}\right)$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{21}{110}\right)$$ $$e\left(\frac{151}{165}\right)$$ $$e\left(\frac{97}{330}\right)$$ $$e\left(\frac{299}{330}\right)$$ $$e\left(\frac{3}{55}\right)$$
$$\chi_{7623}(47,\cdot)$$ 7623.fz 330 yes $$1$$ $$1$$ $$e\left(\frac{239}{330}\right)$$ $$e\left(\frac{74}{165}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{269}{330}\right)$$ $$e\left(\frac{148}{165}\right)$$ $$e\left(\frac{163}{165}\right)$$ $$e\left(\frac{37}{330}\right)$$ $$e\left(\frac{62}{165}\right)$$
$$\chi_{7623}(50,\cdot)$$ 7623.fn 330 no $$1$$ $$1$$ $$e\left(\frac{31}{165}\right)$$ $$e\left(\frac{62}{165}\right)$$ $$e\left(\frac{133}{330}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{157}{330}\right)$$ $$e\left(\frac{124}{165}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{257}{330}\right)$$
$$\chi_{7623}(52,\cdot)$$ 7623.fe 330 yes $$1$$ $$1$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{151}{330}\right)$$ $$e\left(\frac{89}{110}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{67}{165}\right)$$ $$e\left(\frac{41}{55}\right)$$ $$e\left(\frac{8}{165}\right)$$ $$e\left(\frac{91}{165}\right)$$ $$e\left(\frac{109}{330}\right)$$
$$\chi_{7623}(53,\cdot)$$ 7623.fy 330 no $$-1$$ $$1$$ $$e\left(\frac{263}{330}\right)$$ $$e\left(\frac{98}{165}\right)$$ $$e\left(\frac{47}{330}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{31}{165}\right)$$ $$e\left(\frac{127}{330}\right)$$ $$e\left(\frac{52}{165}\right)$$ $$e\left(\frac{81}{110}\right)$$
$$\chi_{7623}(58,\cdot)$$ 7623.fb 165 yes $$1$$ $$1$$ $$e\left(\frac{9}{55}\right)$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{73}{165}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{32}{165}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{58}{165}\right)$$ $$e\left(\frac{41}{165}\right)$$ $$e\left(\frac{127}{165}\right)$$
$$\chi_{7623}(59,\cdot)$$ 7623.fz 330 yes $$1$$ $$1$$ $$e\left(\frac{151}{330}\right)$$ $$e\left(\frac{151}{165}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{181}{330}\right)$$ $$e\left(\frac{137}{165}\right)$$ $$e\left(\frac{152}{165}\right)$$ $$e\left(\frac{323}{330}\right)$$ $$e\left(\frac{73}{165}\right)$$
$$\chi_{7623}(61,\cdot)$$ 7623.fp 330 yes $$1$$ $$1$$ $$e\left(\frac{107}{330}\right)$$ $$e\left(\frac{107}{165}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{107}{110}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{151}{165}\right)$$ $$e\left(\frac{49}{165}\right)$$ $$e\left(\frac{64}{165}\right)$$ $$e\left(\frac{68}{165}\right)$$ $$e\left(\frac{157}{330}\right)$$
$$\chi_{7623}(62,\cdot)$$ 7623.ex 110 no $$-1$$ $$1$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{9}{55}\right)$$ $$e\left(\frac{83}{110}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$