Properties

Modulus $605$
Structure \(C_{220}\times C_{2}\)
Order $440$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(605)
 
pari: g = idealstar(,605,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{220}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{605}(122,\cdot)$, $\chi_{605}(486,\cdot)$

First 32 of 440 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{605}(1,\cdot)\) 605.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{605}(2,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{57}{220}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{171}{220}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{63}{110}\right)\)
\(\chi_{605}(3,\cdot)\) 605.l 20 no \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{605}(4,\cdot)\) 605.u 110 yes \(1\) \(1\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{8}{55}\right)\)
\(\chi_{605}(6,\cdot)\) 605.t 110 no \(-1\) \(1\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{26}{55}\right)\)
\(\chi_{605}(7,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{207}{220}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{39}{220}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{605}(8,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{171}{220}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{207}{220}\right)\) \(e\left(\frac{73}{220}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{79}{110}\right)\)
\(\chi_{605}(9,\cdot)\) 605.j 10 no \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{605}(12,\cdot)\) 605.q 44 yes \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(-i\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(-1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{605}(13,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{39}{220}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{217}{220}\right)\) \(e\left(\frac{93}{110}\right)\)
\(\chi_{605}(14,\cdot)\) 605.u 110 yes \(1\) \(1\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{32}{55}\right)\)
\(\chi_{605}(16,\cdot)\) 605.s 55 no \(1\) \(1\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{16}{55}\right)\)
\(\chi_{605}(17,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{19}{220}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{7}{110}\right)\)
\(\chi_{605}(18,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{79}{220}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{3}{220}\right)\) \(e\left(\frac{17}{220}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{169}{220}\right)\) \(e\left(\frac{41}{110}\right)\)
\(\chi_{605}(19,\cdot)\) 605.v 110 yes \(-1\) \(1\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{2}{55}\right)\)
\(\chi_{605}(21,\cdot)\) 605.p 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{605}(23,\cdot)\) 605.q 44 yes \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(i\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(-1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{605}(24,\cdot)\) 605.v 110 yes \(-1\) \(1\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{34}{55}\right)\)
\(\chi_{605}(26,\cdot)\) 605.s 55 no \(1\) \(1\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{23}{55}\right)\)
\(\chi_{605}(27,\cdot)\) 605.l 20 no \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{605}(28,\cdot)\) 605.w 220 yes \(1\) \(1\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{17}{110}\right)\)
\(\chi_{605}(29,\cdot)\) 605.v 110 yes \(-1\) \(1\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{13}{55}\right)\)
\(\chi_{605}(31,\cdot)\) 605.s 55 no \(1\) \(1\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{14}{55}\right)\)
\(\chi_{605}(32,\cdot)\) 605.r 44 yes \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(-i\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(-1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{605}(34,\cdot)\) 605.o 22 yes \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(-1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{605}(36,\cdot)\) 605.s 55 no \(1\) \(1\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{52}{55}\right)\)
\(\chi_{605}(37,\cdot)\) 605.x 220 yes \(-1\) \(1\) \(e\left(\frac{139}{220}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{61}{110}\right)\)
\(\chi_{605}(38,\cdot)\) 605.x 220 yes \(-1\) \(1\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{21}{220}\right)\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{83}{220}\right)\) \(e\left(\frac{67}{110}\right)\)
\(\chi_{605}(39,\cdot)\) 605.v 110 yes \(-1\) \(1\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{41}{55}\right)\)
\(\chi_{605}(41,\cdot)\) 605.t 110 no \(-1\) \(1\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{37}{55}\right)\)
\(\chi_{605}(42,\cdot)\) 605.x 220 yes \(-1\) \(1\) \(e\left(\frac{27}{220}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{79}{220}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{53}{110}\right)\)
\(\chi_{605}(43,\cdot)\) 605.r 44 yes \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(i\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(-1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\)