Properties

Modulus 9450
Structure \(C_{180}\times C_{6}\times C_{2}\)
Order 2160

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(9450)
pari: g = idealstar(,9450,2)

Character group

sage: G.order()
pari: g.no
Order = 2160
sage: H.invariants()
pari: g.cyc
Structure = \(C_{180}\times C_{6}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{9450}(5927,\cdot)$, $\chi_{9450}(5399,\cdot)$, $\chi_{9450}(8749,\cdot)$

First 32 of 2160 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 11 13 17 19 23 29 31 37 41 43
\(\chi_{9450}(1,\cdot)\) 9450.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{9450}(11,\cdot)\) 9450.gv 90 No \(-1\) \(1\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{9450}(13,\cdot)\) 9450.hh 180 No \(1\) \(1\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{9450}(17,\cdot)\) 9450.gc 60 No \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{9450}(19,\cdot)\) 9450.dy 30 No \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9450}(23,\cdot)\) 9450.hi 180 No \(1\) \(1\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{79}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{9450}(29,\cdot)\) 9450.gs 90 No \(-1\) \(1\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(31,\cdot)\) 9450.gg 90 No \(-1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{9450}(37,\cdot)\) 9450.fw 60 No \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{9450}(41,\cdot)\) 9450.gq 90 No \(1\) \(1\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{9450}(43,\cdot)\) 9450.fe 36 No \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{9450}(47,\cdot)\) 9450.he 180 No \(-1\) \(1\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{137}{180}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{53}{180}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{9450}(53,\cdot)\) 9450.fq 60 No \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{9450}(59,\cdot)\) 9450.gj 90 No \(1\) \(1\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{9450}(61,\cdot)\) 9450.gg 90 No \(-1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{9450}(67,\cdot)\) 9450.hc 180 No \(-1\) \(1\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{9450}(71,\cdot)\) 9450.eh 30 No \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{9450}(73,\cdot)\) 9450.fy 60 No \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{9450}(79,\cdot)\) 9450.gn 90 No \(1\) \(1\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{9450}(83,\cdot)\) 9450.hf 180 No \(-1\) \(1\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{9450}(89,\cdot)\) 9450.ew 30 No \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9450}(97,\cdot)\) 9450.hh 180 No \(1\) \(1\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{9450}(101,\cdot)\) 9450.dp 18 No \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(1\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{9450}(103,\cdot)\) 9450.gz 180 No \(1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{9450}(107,\cdot)\) 9450.cp 12 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-i\)
\(\chi_{9450}(109,\cdot)\) 9450.et 30 No \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\)
\(\chi_{9450}(113,\cdot)\) 9450.hb 180 No \(1\) \(1\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{91}{180}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{9450}(121,\cdot)\) 9450.fk 45 No \(1\) \(1\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{9450}(127,\cdot)\) 9450.ga 60 No \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{9450}(131,\cdot)\) 9450.gf 90 No \(1\) \(1\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{9450}(137,\cdot)\) 9450.hi 180 No \(1\) \(1\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{9450}(139,\cdot)\) 9450.gp 90 No \(-1\) \(1\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{17}{18}\right)\)