# Properties

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

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 $$-1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$