Properties

Modulus $1900$
Structure \(C_{2}\times C_{2}\times C_{180}\)
Order $720$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1900)
 
pari: g = idealstar(,1900,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 720
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{180}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1900}(951,\cdot)$, $\chi_{1900}(77,\cdot)$, $\chi_{1900}(401,\cdot)$

First 32 of 720 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{1900}(1,\cdot)\) 1900.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1900}(3,\cdot)\) 1900.cr 180 yes \(-1\) \(1\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{44}{45}\right)\)
\(\chi_{1900}(7,\cdot)\) 1900.bd 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1900}(9,\cdot)\) 1900.co 90 no \(1\) \(1\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{45}\right)\)
\(\chi_{1900}(11,\cdot)\) 1900.bu 30 yes \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(-1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1900}(13,\cdot)\) 1900.cs 180 no \(1\) \(1\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{79}{180}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{28}{45}\right)\)
\(\chi_{1900}(17,\cdot)\) 1900.ct 180 no \(-1\) \(1\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{67}{90}\right)\)
\(\chi_{1900}(21,\cdot)\) 1900.cl 90 no \(-1\) \(1\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{90}\right)\)
\(\chi_{1900}(23,\cdot)\) 1900.cq 180 yes \(1\) \(1\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{89}{90}\right)\)
\(\chi_{1900}(27,\cdot)\) 1900.ch 60 yes \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(-i\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1900}(29,\cdot)\) 1900.cp 90 no \(-1\) \(1\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{90}\right)\)
\(\chi_{1900}(31,\cdot)\) 1900.by 30 yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(-1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1900}(33,\cdot)\) 1900.cs 180 no \(1\) \(1\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{151}{180}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{41}{45}\right)\)
\(\chi_{1900}(37,\cdot)\) 1900.bq 20 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1900}(39,\cdot)\) 1900.y 10 no \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1900}(41,\cdot)\) 1900.cl 90 no \(-1\) \(1\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{61}{90}\right)\)
\(\chi_{1900}(43,\cdot)\) 1900.cd 36 no \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{1900}(47,\cdot)\) 1900.cq 180 yes \(1\) \(1\) \(e\left(\frac{41}{180}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{89}{180}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{23}{90}\right)\)
\(\chi_{1900}(49,\cdot)\) 1900.s 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1900}(51,\cdot)\) 1900.bn 18 no \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{1900}(53,\cdot)\) 1900.cs 180 no \(1\) \(1\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{4}{45}\right)\)
\(\chi_{1900}(59,\cdot)\) 1900.cj 90 yes \(1\) \(1\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{31}{90}\right)\)
\(\chi_{1900}(61,\cdot)\) 1900.ce 45 no \(1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{22}{45}\right)\)
\(\chi_{1900}(63,\cdot)\) 1900.cq 180 yes \(1\) \(1\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{169}{180}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{91}{180}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{90}\right)\)
\(\chi_{1900}(67,\cdot)\) 1900.cr 180 yes \(-1\) \(1\) \(e\left(\frac{59}{180}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{97}{180}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{16}{45}\right)\)
\(\chi_{1900}(69,\cdot)\) 1900.bx 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(-1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1900}(71,\cdot)\) 1900.cn 90 yes \(1\) \(1\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{73}{90}\right)\)
\(\chi_{1900}(73,\cdot)\) 1900.ct 180 no \(-1\) \(1\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{101}{180}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{89}{180}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{79}{90}\right)\)
\(\chi_{1900}(77,\cdot)\) 1900.bp 20 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1900}(79,\cdot)\) 1900.cj 90 yes \(1\) \(1\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{43}{90}\right)\)
\(\chi_{1900}(81,\cdot)\) 1900.ce 45 no \(1\) \(1\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{41}{45}\right)\)
\(\chi_{1900}(83,\cdot)\) 1900.ci 60 yes \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(i\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
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