Properties

Modulus $9800$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{420}\)
Order $3360$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(9800)
 
pari: g = idealstar(,9800,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 3360
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{420}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{9800}(7351,\cdot)$, $\chi_{9800}(4901,\cdot)$, $\chi_{9800}(1177,\cdot)$, $\chi_{9800}(5001,\cdot)$

First 32 of 3360 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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{9800}(1,\cdot)\) 9800.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{9800}(3,\cdot)\) 9800.hf 420 yes \(-1\) \(1\) \(e\left(\frac{199}{420}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{131}{140}\right)\) \(e\left(\frac{61}{420}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{107}{420}\right)\) \(e\left(\frac{59}{140}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{9800}(9,\cdot)\) 9800.gv 210 no \(1\) \(1\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{61}{210}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{107}{210}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{9800}(11,\cdot)\) 9800.go 210 yes \(-1\) \(1\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{103}{210}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{9800}(13,\cdot)\) 9800.gi 140 yes \(1\) \(1\) \(e\left(\frac{131}{140}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{67}{140}\right)\) \(e\left(\frac{139}{140}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{113}{140}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(17,\cdot)\) 9800.he 420 no \(1\) \(1\) \(e\left(\frac{61}{420}\right)\) \(e\left(\frac{61}{210}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{139}{140}\right)\) \(e\left(\frac{139}{420}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{323}{420}\right)\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{9800}(19,\cdot)\) 9800.eh 30 no \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{9800}(23,\cdot)\) 9800.hi 420 no \(1\) \(1\) \(e\left(\frac{107}{420}\right)\) \(e\left(\frac{107}{210}\right)\) \(e\left(\frac{103}{210}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{323}{420}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{391}{420}\right)\) \(e\left(\frac{107}{140}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{9800}(27,\cdot)\) 9800.gk 140 yes \(-1\) \(1\) \(e\left(\frac{59}{140}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{113}{140}\right)\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{107}{140}\right)\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(29,\cdot)\) 9800.fs 70 yes \(1\) \(1\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(31,\cdot)\) 9800.ef 30 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{9800}(33,\cdot)\) 9800.he 420 no \(1\) \(1\) \(e\left(\frac{11}{420}\right)\) \(e\left(\frac{11}{210}\right)\) \(e\left(\frac{47}{105}\right)\) \(e\left(\frac{9}{140}\right)\) \(e\left(\frac{149}{420}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{313}{420}\right)\) \(e\left(\frac{11}{140}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{9800}(37,\cdot)\) 9800.hj 420 yes \(-1\) \(1\) \(e\left(\frac{173}{420}\right)\) \(e\left(\frac{173}{210}\right)\) \(e\left(\frac{37}{210}\right)\) \(e\left(\frac{27}{140}\right)\) \(e\left(\frac{377}{420}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{379}{420}\right)\) \(e\left(\frac{33}{140}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{9800}(39,\cdot)\) 9800.gq 210 no \(-1\) \(1\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{143}{210}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{9800}(41,\cdot)\) 9800.fm 70 no \(-1\) \(1\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{9800}(43,\cdot)\) 9800.dm 28 no \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\)
\(\chi_{9800}(47,\cdot)\) 9800.hg 420 no \(-1\) \(1\) \(e\left(\frac{239}{420}\right)\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{11}{140}\right)\) \(e\left(\frac{11}{420}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{157}{420}\right)\) \(e\left(\frac{99}{140}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{9800}(51,\cdot)\) 9800.ex 42 no \(-1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(53,\cdot)\) 9800.hj 420 yes \(-1\) \(1\) \(e\left(\frac{79}{420}\right)\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{131}{210}\right)\) \(e\left(\frac{1}{140}\right)\) \(e\left(\frac{211}{420}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{377}{420}\right)\) \(e\left(\frac{79}{140}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{9800}(57,\cdot)\) 9800.dn 28 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{9800}(59,\cdot)\) 9800.gn 210 yes \(1\) \(1\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{61}{105}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{101}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{9800}(61,\cdot)\) 9800.gt 210 yes \(-1\) \(1\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{163}{210}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{9800}(67,\cdot)\) 9800.fd 60 no \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{9800}(69,\cdot)\) 9800.fh 70 yes \(-1\) \(1\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{9800}(71,\cdot)\) 9800.fk 70 no \(-1\) \(1\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{9800}(73,\cdot)\) 9800.he 420 no \(1\) \(1\) \(e\left(\frac{307}{420}\right)\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{73}{140}\right)\) \(e\left(\frac{73}{420}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{221}{420}\right)\) \(e\left(\frac{27}{140}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{9800}(79,\cdot)\) 9800.ee 30 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{9800}(81,\cdot)\) 9800.ge 105 no \(1\) \(1\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{83}{105}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{61}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{9800}(83,\cdot)\) 9800.gk 140 yes \(-1\) \(1\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{59}{140}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{41}{140}\right)\) \(e\left(\frac{111}{140}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(87,\cdot)\) 9800.hg 420 no \(-1\) \(1\) \(e\left(\frac{43}{420}\right)\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{167}{210}\right)\) \(e\left(\frac{67}{140}\right)\) \(e\left(\frac{67}{420}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{269}{420}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{9800}(89,\cdot)\) 9800.gp 210 no \(-1\) \(1\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{210}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{9800}(93,\cdot)\) 9800.fw 84 no \(-1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
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