Properties

Modulus $1470$
Structure \(C_{84}\times C_{2}\times C_{2}\)
Order $336$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1470)
 
pari: g = idealstar(,1470,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 336
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1470}(491,\cdot)$, $\chi_{1470}(1177,\cdot)$, $\chi_{1470}(1081,\cdot)$

First 32 of 336 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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1470}(1,\cdot)\) 1470.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1470}(11,\cdot)\) 1470.bl 42 no \(-1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1470}(13,\cdot)\) 1470.bi 28 no \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{1470}(17,\cdot)\) 1470.bs 84 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(19,\cdot)\) 1470.p 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)
\(\chi_{1470}(23,\cdot)\) 1470.bt 84 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{1470}(29,\cdot)\) 1470.bf 14 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{1470}(31,\cdot)\) 1470.o 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)
\(\chi_{1470}(37,\cdot)\) 1470.bv 84 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(41,\cdot)\) 1470.be 14 no \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1470}(43,\cdot)\) 1470.bh 28 no \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{1470}(47,\cdot)\) 1470.bs 84 no \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{1470}(53,\cdot)\) 1470.bt 84 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{1470}(59,\cdot)\) 1470.bm 42 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{1470}(61,\cdot)\) 1470.br 42 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{1470}(67,\cdot)\) 1470.w 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-i\)
\(\chi_{1470}(71,\cdot)\) 1470.bd 14 no \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1470}(73,\cdot)\) 1470.bu 84 no \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(79,\cdot)\) 1470.n 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)
\(\chi_{1470}(83,\cdot)\) 1470.bk 28 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(89,\cdot)\) 1470.bm 42 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{1470}(97,\cdot)\) 1470.m 4 no \(1\) \(1\) \(1\) \(i\) \(-i\) \(1\) \(-i\) \(-1\) \(-1\) \(i\) \(-1\) \(-i\)
\(\chi_{1470}(101,\cdot)\) 1470.bo 42 no \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1470}(103,\cdot)\) 1470.bu 84 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{1470}(107,\cdot)\) 1470.bt 84 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{1470}(109,\cdot)\) 1470.bq 42 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{1470}(113,\cdot)\) 1470.bj 28 no \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{1470}(121,\cdot)\) 1470.bg 21 no \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1470}(127,\cdot)\) 1470.bh 28 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(-1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1470}(131,\cdot)\) 1470.bo 42 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1470}(137,\cdot)\) 1470.bt 84 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{1470}(139,\cdot)\) 1470.z 14 no \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{9}{14}\right)\)