# Properties

 Modulus $3267$ Structure $$C_{2}\times C_{990}$$ Order $1980$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3267)

pari: g = idealstar(,3267,2)

## Character group

 sage: G.order()  pari: g.no Order = 1980 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{990}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3267}(3026,\cdot)$, $\chi_{3267}(244,\cdot)$

## First 32 of 1980 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$13$$ $$14$$ $$16$$ $$17$$
$$\chi_{3267}(1,\cdot)$$ 3267.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3267}(2,\cdot)$$ 3267.bt 990 yes $$1$$ $$1$$ $$e\left(\frac{32}{495}\right)$$ $$e\left(\frac{64}{495}\right)$$ $$e\left(\frac{941}{990}\right)$$ $$e\left(\frac{943}{990}\right)$$ $$e\left(\frac{32}{165}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{359}{990}\right)$$ $$e\left(\frac{17}{990}\right)$$ $$e\left(\frac{128}{495}\right)$$ $$e\left(\frac{46}{165}\right)$$
$$\chi_{3267}(4,\cdot)$$ 3267.bs 495 yes $$1$$ $$1$$ $$e\left(\frac{64}{495}\right)$$ $$e\left(\frac{128}{495}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{448}{495}\right)$$ $$e\left(\frac{64}{165}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{359}{495}\right)$$ $$e\left(\frac{17}{495}\right)$$ $$e\left(\frac{256}{495}\right)$$ $$e\left(\frac{92}{165}\right)$$
$$\chi_{3267}(5,\cdot)$$ 3267.bv 990 yes $$-1$$ $$1$$ $$e\left(\frac{941}{990}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{169}{990}\right)$$ $$e\left(\frac{76}{495}\right)$$ $$e\left(\frac{281}{330}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{83}{495}\right)$$ $$e\left(\frac{103}{990}\right)$$ $$e\left(\frac{397}{495}\right)$$ $$e\left(\frac{43}{330}\right)$$
$$\chi_{3267}(7,\cdot)$$ 3267.bu 990 yes $$-1$$ $$1$$ $$e\left(\frac{943}{990}\right)$$ $$e\left(\frac{448}{495}\right)$$ $$e\left(\frac{76}{495}\right)$$ $$e\left(\frac{661}{990}\right)$$ $$e\left(\frac{283}{330}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{533}{990}\right)$$ $$e\left(\frac{307}{495}\right)$$ $$e\left(\frac{401}{495}\right)$$ $$e\left(\frac{149}{330}\right)$$
$$\chi_{3267}(8,\cdot)$$ 3267.bp 330 no $$1$$ $$1$$ $$e\left(\frac{32}{165}\right)$$ $$e\left(\frac{64}{165}\right)$$ $$e\left(\frac{281}{330}\right)$$ $$e\left(\frac{283}{330}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{330}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{128}{165}\right)$$ $$e\left(\frac{46}{55}\right)$$
$$\chi_{3267}(10,\cdot)$$ 3267.bc 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{3267}(13,\cdot)$$ 3267.bu 990 yes $$-1$$ $$1$$ $$e\left(\frac{359}{990}\right)$$ $$e\left(\frac{359}{495}\right)$$ $$e\left(\frac{83}{495}\right)$$ $$e\left(\frac{533}{990}\right)$$ $$e\left(\frac{29}{330}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{289}{990}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{223}{495}\right)$$ $$e\left(\frac{217}{330}\right)$$
$$\chi_{3267}(14,\cdot)$$ 3267.bv 990 yes $$-1$$ $$1$$ $$e\left(\frac{17}{990}\right)$$ $$e\left(\frac{17}{495}\right)$$ $$e\left(\frac{103}{990}\right)$$ $$e\left(\frac{307}{495}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{631}{990}\right)$$ $$e\left(\frac{34}{495}\right)$$ $$e\left(\frac{241}{330}\right)$$
$$\chi_{3267}(16,\cdot)$$ 3267.bs 495 yes $$1$$ $$1$$ $$e\left(\frac{128}{495}\right)$$ $$e\left(\frac{256}{495}\right)$$ $$e\left(\frac{397}{495}\right)$$ $$e\left(\frac{401}{495}\right)$$ $$e\left(\frac{128}{165}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{223}{495}\right)$$ $$e\left(\frac{34}{495}\right)$$ $$e\left(\frac{17}{495}\right)$$ $$e\left(\frac{19}{165}\right)$$
$$\chi_{3267}(17,\cdot)$$ 3267.bp 330 no $$1$$ $$1$$ $$e\left(\frac{46}{165}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{43}{330}\right)$$ $$e\left(\frac{149}{330}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{217}{330}\right)$$ $$e\left(\frac{241}{330}\right)$$ $$e\left(\frac{19}{165}\right)$$ $$e\left(\frac{18}{55}\right)$$
$$\chi_{3267}(19,\cdot)$$ 3267.bq 330 no $$-1$$ $$1$$ $$e\left(\frac{139}{330}\right)$$ $$e\left(\frac{139}{165}\right)$$ $$e\left(\frac{28}{165}\right)$$ $$e\left(\frac{313}{330}\right)$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{179}{330}\right)$$ $$e\left(\frac{61}{165}\right)$$ $$e\left(\frac{113}{165}\right)$$ $$e\left(\frac{107}{110}\right)$$
$$\chi_{3267}(20,\cdot)$$ 3267.bv 990 yes $$-1$$ $$1$$ $$e\left(\frac{79}{990}\right)$$ $$e\left(\frac{79}{495}\right)$$ $$e\left(\frac{71}{990}\right)$$ $$e\left(\frac{29}{495}\right)$$ $$e\left(\frac{79}{330}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{442}{495}\right)$$ $$e\left(\frac{137}{990}\right)$$ $$e\left(\frac{158}{495}\right)$$ $$e\left(\frac{227}{330}\right)$$
$$\chi_{3267}(23,\cdot)$$ 3267.bn 198 yes $$-1$$ $$1$$ $$e\left(\frac{49}{198}\right)$$ $$e\left(\frac{49}{99}\right)$$ $$e\left(\frac{29}{198}\right)$$ $$e\left(\frac{23}{99}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{16}{99}\right)$$ $$e\left(\frac{95}{198}\right)$$ $$e\left(\frac{98}{99}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{3267}(25,\cdot)$$ 3267.bs 495 yes $$1$$ $$1$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{397}{495}\right)$$ $$e\left(\frac{169}{495}\right)$$ $$e\left(\frac{152}{495}\right)$$ $$e\left(\frac{116}{165}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{166}{495}\right)$$ $$e\left(\frac{103}{495}\right)$$ $$e\left(\frac{299}{495}\right)$$ $$e\left(\frac{43}{165}\right)$$
$$\chi_{3267}(26,\cdot)$$ 3267.bi 110 no $$-1$$ $$1$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{13}{110}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{101}{110}\right)$$ $$e\left(\frac{39}{55}\right)$$ $$e\left(\frac{103}{110}\right)$$
$$\chi_{3267}(28,\cdot)$$ 3267.bj 110 no $$-1$$ $$1$$ $$e\left(\frac{9}{110}\right)$$ $$e\left(\frac{9}{55}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{63}{110}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{1}{110}\right)$$
$$\chi_{3267}(29,\cdot)$$ 3267.bt 990 yes $$1$$ $$1$$ $$e\left(\frac{104}{495}\right)$$ $$e\left(\frac{208}{495}\right)$$ $$e\left(\frac{707}{990}\right)$$ $$e\left(\frac{961}{990}\right)$$ $$e\left(\frac{104}{165}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{53}{990}\right)$$ $$e\left(\frac{179}{990}\right)$$ $$e\left(\frac{416}{495}\right)$$ $$e\left(\frac{67}{165}\right)$$
$$\chi_{3267}(31,\cdot)$$ 3267.bs 495 yes $$1$$ $$1$$ $$e\left(\frac{442}{495}\right)$$ $$e\left(\frac{389}{495}\right)$$ $$e\left(\frac{203}{495}\right)$$ $$e\left(\frac{124}{495}\right)$$ $$e\left(\frac{112}{165}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{422}{495}\right)$$ $$e\left(\frac{71}{495}\right)$$ $$e\left(\frac{283}{495}\right)$$ $$e\left(\frac{161}{165}\right)$$
$$\chi_{3267}(32,\cdot)$$ 3267.bo 198 yes $$1$$ $$1$$ $$e\left(\frac{32}{99}\right)$$ $$e\left(\frac{64}{99}\right)$$ $$e\left(\frac{149}{198}\right)$$ $$e\left(\frac{151}{198}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{161}{198}\right)$$ $$e\left(\frac{17}{198}\right)$$ $$e\left(\frac{29}{99}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{3267}(34,\cdot)$$ 3267.bh 99 yes $$1$$ $$1$$ $$e\left(\frac{34}{99}\right)$$ $$e\left(\frac{68}{99}\right)$$ $$e\left(\frac{8}{99}\right)$$ $$e\left(\frac{40}{99}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{99}\right)$$ $$e\left(\frac{74}{99}\right)$$ $$e\left(\frac{37}{99}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{3267}(35,\cdot)$$ 3267.bp 330 no $$1$$ $$1$$ $$e\left(\frac{149}{165}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{107}{330}\right)$$ $$e\left(\frac{271}{330}\right)$$ $$e\left(\frac{39}{55}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{233}{330}\right)$$ $$e\left(\frac{239}{330}\right)$$ $$e\left(\frac{101}{165}\right)$$ $$e\left(\frac{32}{55}\right)$$
$$\chi_{3267}(37,\cdot)$$ 3267.bl 165 no $$1$$ $$1$$ $$e\left(\frac{118}{165}\right)$$ $$e\left(\frac{71}{165}\right)$$ $$e\left(\frac{152}{165}\right)$$ $$e\left(\frac{1}{165}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{38}{165}\right)$$ $$e\left(\frac{119}{165}\right)$$ $$e\left(\frac{142}{165}\right)$$ $$e\left(\frac{39}{55}\right)$$
$$\chi_{3267}(38,\cdot)$$ 3267.bv 990 yes $$-1$$ $$1$$ $$e\left(\frac{481}{990}\right)$$ $$e\left(\frac{481}{495}\right)$$ $$e\left(\frac{119}{990}\right)$$ $$e\left(\frac{446}{495}\right)$$ $$e\left(\frac{151}{330}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{448}{495}\right)$$ $$e\left(\frac{383}{990}\right)$$ $$e\left(\frac{467}{495}\right)$$ $$e\left(\frac{83}{330}\right)$$
$$\chi_{3267}(40,\cdot)$$ 3267.bf 90 no $$-1$$ $$1$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{3267}(41,\cdot)$$ 3267.bt 990 yes $$1$$ $$1$$ $$e\left(\frac{76}{495}\right)$$ $$e\left(\frac{152}{495}\right)$$ $$e\left(\frac{193}{990}\right)$$ $$e\left(\frac{569}{990}\right)$$ $$e\left(\frac{76}{165}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{667}{990}\right)$$ $$e\left(\frac{721}{990}\right)$$ $$e\left(\frac{304}{495}\right)$$ $$e\left(\frac{68}{165}\right)$$
$$\chi_{3267}(43,\cdot)$$ 3267.bm 198 yes $$-1$$ $$1$$ $$e\left(\frac{89}{198}\right)$$ $$e\left(\frac{89}{99}\right)$$ $$e\left(\frac{92}{99}\right)$$ $$e\left(\frac{29}{198}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{145}{198}\right)$$ $$e\left(\frac{59}{99}\right)$$ $$e\left(\frac{79}{99}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{3267}(46,\cdot)$$ 3267.bq 330 no $$-1$$ $$1$$ $$e\left(\frac{103}{330}\right)$$ $$e\left(\frac{103}{165}\right)$$ $$e\left(\frac{16}{165}\right)$$ $$e\left(\frac{61}{330}\right)$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{173}{330}\right)$$ $$e\left(\frac{82}{165}\right)$$ $$e\left(\frac{41}{165}\right)$$ $$e\left(\frac{69}{110}\right)$$
$$\chi_{3267}(47,\cdot)$$ 3267.bv 990 yes $$-1$$ $$1$$ $$e\left(\frac{277}{990}\right)$$ $$e\left(\frac{277}{495}\right)$$ $$e\left(\frac{863}{990}\right)$$ $$e\left(\frac{227}{495}\right)$$ $$e\left(\frac{277}{330}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{46}{495}\right)$$ $$e\left(\frac{731}{990}\right)$$ $$e\left(\frac{59}{495}\right)$$ $$e\left(\frac{161}{330}\right)$$
$$\chi_{3267}(49,\cdot)$$ 3267.bs 495 yes $$1$$ $$1$$ $$e\left(\frac{448}{495}\right)$$ $$e\left(\frac{401}{495}\right)$$ $$e\left(\frac{152}{495}\right)$$ $$e\left(\frac{166}{495}\right)$$ $$e\left(\frac{118}{165}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{38}{495}\right)$$ $$e\left(\frac{119}{495}\right)$$ $$e\left(\frac{307}{495}\right)$$ $$e\left(\frac{149}{165}\right)$$
$$\chi_{3267}(50,\cdot)$$ 3267.bt 990 yes $$1$$ $$1$$ $$e\left(\frac{478}{495}\right)$$ $$e\left(\frac{461}{495}\right)$$ $$e\left(\frac{289}{990}\right)$$ $$e\left(\frac{257}{990}\right)$$ $$e\left(\frac{148}{165}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{691}{990}\right)$$ $$e\left(\frac{223}{990}\right)$$ $$e\left(\frac{427}{495}\right)$$ $$e\left(\frac{89}{165}\right)$$
$$\chi_{3267}(52,\cdot)$$ 3267.bu 990 yes $$-1$$ $$1$$ $$e\left(\frac{487}{990}\right)$$ $$e\left(\frac{487}{495}\right)$$ $$e\left(\frac{34}{495}\right)$$ $$e\left(\frac{439}{990}\right)$$ $$e\left(\frac{157}{330}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{17}{990}\right)$$ $$e\left(\frac{463}{495}\right)$$ $$e\left(\frac{479}{495}\right)$$ $$e\left(\frac{71}{330}\right)$$