Properties

Modulus $1045$
Structure \(C_{180}\times C_{2}\times C_{2}\)
Order $720$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1045)
 
pari: g = idealstar(,1045,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 720
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{180}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1045}(837,\cdot)$, $\chi_{1045}(761,\cdot)$, $\chi_{1045}(496,\cdot)$

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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1045}(1,\cdot)\) 1045.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1045}(2,\cdot)\) 1045.cq 180 yes \(-1\) \(1\) \(e\left(\frac{73}{180}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{31}{45}\right)\)
\(\chi_{1045}(3,\cdot)\) 1045.cr 180 yes \(1\) \(1\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{7}{180}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{43}{45}\right)\)
\(\chi_{1045}(4,\cdot)\) 1045.ck 90 yes \(1\) \(1\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(6,\cdot)\) 1045.cj 90 no \(-1\) \(1\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(7,\cdot)\) 1045.cf 60 yes \(1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(i\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1045}(8,\cdot)\) 1045.cg 60 yes \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(i\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1045}(9,\cdot)\) 1045.ck 90 yes \(1\) \(1\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{41}{45}\right)\)
\(\chi_{1045}(12,\cdot)\) 1045.bd 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(i\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1045}(13,\cdot)\) 1045.cq 180 yes \(-1\) \(1\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(14,\cdot)\) 1045.cl 90 yes \(-1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{11}{90}\right)\)
\(\chi_{1045}(16,\cdot)\) 1045.ce 45 no \(1\) \(1\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(17,\cdot)\) 1045.cs 180 yes \(1\) \(1\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{31}{180}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{53}{90}\right)\)
\(\chi_{1045}(18,\cdot)\) 1045.br 20 yes \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1045}(21,\cdot)\) 1045.bm 18 no \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{1045}(23,\cdot)\) 1045.ca 36 no \(-1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{1045}(24,\cdot)\) 1045.cp 90 yes \(-1\) \(1\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{45}\right)\)
\(\chi_{1045}(26,\cdot)\) 1045.bh 15 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1045}(27,\cdot)\) 1045.ci 60 yes \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(-i\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1045}(28,\cdot)\) 1045.cs 180 yes \(1\) \(1\) \(e\left(\frac{17}{180}\right)\) \(e\left(\frac{41}{180}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{73}{90}\right)\)
\(\chi_{1045}(29,\cdot)\) 1045.cn 90 yes \(1\) \(1\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{19}{90}\right)\)
\(\chi_{1045}(31,\cdot)\) 1045.bt 30 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(-1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1045}(32,\cdot)\) 1045.cd 36 yes \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{1045}(34,\cdot)\) 1045.bl 18 no \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{1045}(36,\cdot)\) 1045.ce 45 no \(1\) \(1\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{13}{45}\right)\)
\(\chi_{1045}(37,\cdot)\) 1045.bp 20 yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1045}(39,\cdot)\) 1045.x 10 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1045}(41,\cdot)\) 1045.cm 90 no \(1\) \(1\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{41}{90}\right)\)
\(\chi_{1045}(42,\cdot)\) 1045.ct 180 yes \(-1\) \(1\) \(e\left(\frac{173}{180}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{7}{90}\right)\)
\(\chi_{1045}(43,\cdot)\) 1045.cb 36 yes \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{1045}(46,\cdot)\) 1045.by 30 no \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(-1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1045}(47,\cdot)\) 1045.ct 180 yes \(-1\) \(1\) \(e\left(\frac{89}{180}\right)\) \(e\left(\frac{167}{180}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{1}{90}\right)\)