Properties

Modulus $1840$
Structure \(C_{44}\times C_{4}\times C_{2}\times C_{2}\)
Order $704$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1840)
 
pari: g = idealstar(,1840,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 704
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{44}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1840}(1151,\cdot)$, $\chi_{1840}(1381,\cdot)$, $\chi_{1840}(737,\cdot)$, $\chi_{1840}(1201,\cdot)$

First 32 of 704 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(27\) \(29\)
\(\chi_{1840}(1,\cdot)\) 1840.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1840}(3,\cdot)\) 1840.ch 44 yes \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{1840}(7,\cdot)\) 1840.cq 44 no \(-1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{1840}(9,\cdot)\) 1840.bv 22 no \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{1840}(11,\cdot)\) 1840.cw 44 no \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{1840}(13,\cdot)\) 1840.db 44 yes \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{1840}(17,\cdot)\) 1840.ct 44 no \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{1840}(19,\cdot)\) 1840.cj 44 yes \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{1840}(21,\cdot)\) 1840.cl 44 no \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{1840}(27,\cdot)\) 1840.ch 44 yes \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{1840}(29,\cdot)\) 1840.ck 44 yes \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{1840}(31,\cdot)\) 1840.cc 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{1840}(33,\cdot)\) 1840.ct 44 no \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{1840}(37,\cdot)\) 1840.da 44 yes \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{1840}(39,\cdot)\) 1840.bx 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{1840}(41,\cdot)\) 1840.bz 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{1840}(43,\cdot)\) 1840.cz 44 yes \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{1840}(47,\cdot)\) 1840.ba 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(1\) \(-i\) \(-1\)
\(\chi_{1840}(49,\cdot)\) 1840.ca 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{1840}(51,\cdot)\) 1840.cw 44 no \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{1840}(53,\cdot)\) 1840.cf 44 yes \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{1840}(57,\cdot)\) 1840.cm 44 no \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{1840}(59,\cdot)\) 1840.cx 44 yes \(-1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{1840}(61,\cdot)\) 1840.cl 44 no \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{1840}(63,\cdot)\) 1840.cp 44 no \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{1840}(67,\cdot)\) 1840.cz 44 yes \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{1840}(71,\cdot)\) 1840.bt 22 no \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{1840}(73,\cdot)\) 1840.cs 44 no \(-1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{1840}(77,\cdot)\) 1840.ce 44 yes \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{1840}(79,\cdot)\) 1840.bs 22 no \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{1840}(81,\cdot)\) 1840.bo 11 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{1840}(83,\cdot)\) 1840.cg 44 yes \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{44}\right)\)