Properties

Modulus $2450$
Structure \(C_{2}\times C_{420}\)
Order $840$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2450)
 
pari: g = idealstar(,2450,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 840
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{420}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2450}(1177,\cdot)$, $\chi_{2450}(101,\cdot)$

First 32 of 840 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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{2450}(1,\cdot)\) 2450.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2450}(3,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{199}{420}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{61}{420}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{317}{420}\right)\) \(e\left(\frac{59}{140}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{2450}(9,\cdot)\) 2450.bt 210 no \(1\) \(1\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{61}{210}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{107}{210}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2450}(11,\cdot)\) 2450.bo 105 no \(1\) \(1\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{104}{105}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{2450}(13,\cdot)\) 2450.bp 140 no \(1\) \(1\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{137}{140}\right)\) \(e\left(\frac{139}{140}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2450}(17,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{61}{420}\right)\) \(e\left(\frac{61}{210}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{139}{140}\right)\) \(e\left(\frac{139}{420}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{323}{420}\right)\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{2450}(19,\cdot)\) 2450.bc 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{2450}(23,\cdot)\) 2450.bu 420 no \(-1\) \(1\) \(e\left(\frac{317}{420}\right)\) \(e\left(\frac{107}{210}\right)\) \(e\left(\frac{104}{105}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{323}{420}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{181}{420}\right)\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{2450}(27,\cdot)\) 2450.bp 140 no \(1\) \(1\) \(e\left(\frac{59}{140}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{61}{140}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2450}(29,\cdot)\) 2450.bj 70 no \(1\) \(1\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2450}(31,\cdot)\) 2450.ba 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{2450}(33,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{11}{420}\right)\) \(e\left(\frac{11}{210}\right)\) \(e\left(\frac{47}{105}\right)\) \(e\left(\frac{9}{140}\right)\) \(e\left(\frac{149}{420}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{313}{420}\right)\) \(e\left(\frac{11}{140}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{2450}(37,\cdot)\) 2450.bu 420 no \(-1\) \(1\) \(e\left(\frac{383}{420}\right)\) \(e\left(\frac{173}{210}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{97}{140}\right)\) \(e\left(\frac{377}{420}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{379}{420}\right)\) \(e\left(\frac{103}{140}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2450}(39,\cdot)\) 2450.bt 210 no \(1\) \(1\) \(e\left(\frac{191}{210}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{19}{105}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{210}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{2450}(41,\cdot)\) 2450.bk 70 no \(-1\) \(1\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2450}(43,\cdot)\) 2450.y 28 no \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\)
\(\chi_{2450}(47,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{29}{420}\right)\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{11}{140}\right)\) \(e\left(\frac{11}{420}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{367}{420}\right)\) \(e\left(\frac{29}{140}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{2450}(51,\cdot)\) 2450.x 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2450}(53,\cdot)\) 2450.bu 420 no \(-1\) \(1\) \(e\left(\frac{289}{420}\right)\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{71}{140}\right)\) \(e\left(\frac{211}{420}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{377}{420}\right)\) \(e\left(\frac{9}{140}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{2450}(57,\cdot)\) 2450.y 28 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{2450}(59,\cdot)\) 2450.br 210 no \(-1\) \(1\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{61}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{2450}(61,\cdot)\) 2450.bs 210 no \(-1\) \(1\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{29}{105}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{2450}(67,\cdot)\) 2450.bh 60 no \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2450}(69,\cdot)\) 2450.bl 70 no \(-1\) \(1\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{2450}(71,\cdot)\) 2450.bd 35 no \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2450}(73,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{307}{420}\right)\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{73}{140}\right)\) \(e\left(\frac{73}{420}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{221}{420}\right)\) \(e\left(\frac{27}{140}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{2450}(79,\cdot)\) 2450.bb 30 no \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{2450}(81,\cdot)\) 2450.bo 105 no \(1\) \(1\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{83}{105}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{61}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2450}(83,\cdot)\) 2450.bp 140 no \(1\) \(1\) \(e\left(\frac{37}{140}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{129}{140}\right)\) \(e\left(\frac{43}{140}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{111}{140}\right)\) \(e\left(\frac{111}{140}\right)\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{2450}(87,\cdot)\) 2450.bv 420 no \(1\) \(1\) \(e\left(\frac{253}{420}\right)\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{67}{140}\right)\) \(e\left(\frac{67}{420}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{59}{420}\right)\) \(e\left(\frac{113}{140}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{2450}(89,\cdot)\) 2450.br 210 no \(-1\) \(1\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{210}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{2450}(93,\cdot)\) 2450.bn 84 no \(-1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
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