Properties

Modulus $980$
Structure \(C_{84}\times C_{2}\times C_{2}\)
Order $336$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(980)
 
pari: g = idealstar(,980,2)
 

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 = $\chi_{980}(491,\cdot)$, $\chi_{980}(197,\cdot)$, $\chi_{980}(101,\cdot)$

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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{980}(1,\cdot)\) 980.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{980}(3,\cdot)\) 980.bt 84 yes \(-1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(9,\cdot)\) 980.bn 42 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(11,\cdot)\) 980.bm 42 no \(-1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(13,\cdot)\) 980.bi 28 no \(1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\)
\(\chi_{980}(17,\cdot)\) 980.bu 84 no \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(19,\cdot)\) 980.s 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(23,\cdot)\) 980.bs 84 yes \(1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(27,\cdot)\) 980.bj 28 yes \(-1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(-1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\)
\(\chi_{980}(29,\cdot)\) 980.bd 14 no \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\)
\(\chi_{980}(31,\cdot)\) 980.o 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(33,\cdot)\) 980.bu 84 no \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(37,\cdot)\) 980.bv 84 no \(-1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(39,\cdot)\) 980.bq 42 yes \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(41,\cdot)\) 980.bc 14 no \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\)
\(\chi_{980}(43,\cdot)\) 980.bk 28 yes \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\)
\(\chi_{980}(47,\cdot)\) 980.bt 84 yes \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(51,\cdot)\) 980.bm 42 no \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(53,\cdot)\) 980.bv 84 no \(-1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(57,\cdot)\) 980.bh 28 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{980}(59,\cdot)\) 980.bl 42 yes \(1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(61,\cdot)\) 980.bo 42 no \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(67,\cdot)\) 980.x 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(69,\cdot)\) 980.z 14 no \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\)
\(\chi_{980}(71,\cdot)\) 980.be 14 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\)
\(\chi_{980}(73,\cdot)\) 980.bu 84 no \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(79,\cdot)\) 980.p 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(81,\cdot)\) 980.bg 21 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(83,\cdot)\) 980.bj 28 yes \(-1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\)
\(\chi_{980}(87,\cdot)\) 980.bt 84 yes \(-1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(89,\cdot)\) 980.br 42 no \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(93,\cdot)\) 980.bv 84 no \(-1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{3}\right)\)