Properties

Modulus $211$
Structure \(C_{210}\)
Order $210$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(211)
 
pari: g = idealstar(,211,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 210
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{210}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{211}(2,\cdot)$

First 32 of 210 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{211}(1,\cdot)\) 211.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{211}(2,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{139}{210}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{211}(3,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{169}{210}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{64}{105}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{6}{35}\right)\)
\(\chi_{211}(4,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{35}\right)\)
\(\chi_{211}(5,\cdot)\) 211.l 35 yes \(1\) \(1\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{35}\right)\)
\(\chi_{211}(6,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{33}{35}\right)\)
\(\chi_{211}(7,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{139}{210}\right)\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{97}{105}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{8}{35}\right)\)
\(\chi_{211}(8,\cdot)\) 211.n 70 yes \(-1\) \(1\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{35}\right)\)
\(\chi_{211}(9,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{64}{105}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{97}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{12}{35}\right)\)
\(\chi_{211}(10,\cdot)\) 211.k 30 yes \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{211}(11,\cdot)\) 211.l 35 yes \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{34}{35}\right)\)
\(\chi_{211}(12,\cdot)\) 211.h 14 yes \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{211}(13,\cdot)\) 211.l 35 yes \(1\) \(1\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{211}(14,\cdot)\) 211.c 3 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{211}(15,\cdot)\) 211.e 6 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{211}(16,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{67}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{211}(17,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{157}{210}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{151}{210}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{52}{105}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{18}{35}\right)\)
\(\chi_{211}(18,\cdot)\) 211.n 70 yes \(-1\) \(1\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{35}\right)\)
\(\chi_{211}(19,\cdot)\) 211.i 15 yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{211}(20,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{67}{105}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{29}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{35}\right)\)
\(\chi_{211}(21,\cdot)\) 211.i 15 yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{211}(22,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{163}{210}\right)\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{16}{105}\right)\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{26}{35}\right)\)
\(\chi_{211}(23,\cdot)\) 211.g 10 yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{211}(24,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{67}{105}\right)\) \(e\left(\frac{47}{105}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{35}\right)\)
\(\chi_{211}(25,\cdot)\) 211.l 35 yes \(1\) \(1\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{35}\right)\)
\(\chi_{211}(26,\cdot)\) 211.m 42 yes \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{211}(27,\cdot)\) 211.n 70 yes \(-1\) \(1\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{18}{35}\right)\)
\(\chi_{211}(28,\cdot)\) 211.n 70 yes \(-1\) \(1\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{211}(29,\cdot)\) 211.p 210 yes \(-1\) \(1\) \(e\left(\frac{179}{210}\right)\) \(e\left(\frac{137}{210}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{53}{105}\right)\) \(e\left(\frac{101}{210}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{211}(30,\cdot)\) 211.o 105 yes \(1\) \(1\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{52}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{211}(31,\cdot)\) 211.m 42 yes \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{211}(32,\cdot)\) 211.m 42 yes \(-1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{6}{7}\right)\)
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