Properties

Modulus $1425$
Structure \(C_{2}\times C_{2}\times C_{180}\)
Order $720$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1425)
 
pari: g = idealstar(,1425,2)
 

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 = $\chi_{1425}(476,\cdot)$, $\chi_{1425}(1027,\cdot)$, $\chi_{1425}(1351,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(22\)
\(\chi_{1425}(1,\cdot)\) 1425.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1425}(2,\cdot)\) 1425.cq 180 yes \(-1\) \(1\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{41}{180}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{103}{180}\right)\)
\(\chi_{1425}(4,\cdot)\) 1425.cn 90 no \(1\) \(1\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{13}{90}\right)\)
\(\chi_{1425}(7,\cdot)\) 1425.bg 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(-i\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1425}(8,\cdot)\) 1425.ch 60 yes \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{43}{60}\right)\)
\(\chi_{1425}(11,\cdot)\) 1425.bw 30 yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1425}(13,\cdot)\) 1425.cs 180 no \(1\) \(1\) \(e\left(\frac{41}{180}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{79}{180}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{137}{180}\right)\)
\(\chi_{1425}(14,\cdot)\) 1425.cm 90 yes \(1\) \(1\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{7}{45}\right)\)
\(\chi_{1425}(16,\cdot)\) 1425.ce 45 no \(1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{13}{45}\right)\)
\(\chi_{1425}(17,\cdot)\) 1425.cr 180 yes \(1\) \(1\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{91}{180}\right)\) \(e\left(\frac{49}{180}\right)\)
\(\chi_{1425}(22,\cdot)\) 1425.cs 180 no \(1\) \(1\) \(e\left(\frac{103}{180}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{137}{180}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{151}{180}\right)\)
\(\chi_{1425}(23,\cdot)\) 1425.cr 180 yes \(1\) \(1\) \(e\left(\frac{29}{180}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{137}{180}\right)\) \(e\left(\frac{143}{180}\right)\)
\(\chi_{1425}(26,\cdot)\) 1425.t 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1425}(28,\cdot)\) 1425.ct 180 no \(-1\) \(1\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{157}{180}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{131}{180}\right)\)
\(\chi_{1425}(29,\cdot)\) 1425.cm 90 yes \(1\) \(1\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{44}{45}\right)\)
\(\chi_{1425}(31,\cdot)\) 1425.bv 30 no \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1425}(32,\cdot)\) 1425.cd 36 no \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{31}{36}\right)\)
\(\chi_{1425}(34,\cdot)\) 1425.cp 90 no \(-1\) \(1\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{38}{45}\right)\)
\(\chi_{1425}(37,\cdot)\) 1425.bp 20 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{1425}(41,\cdot)\) 1425.cl 90 yes \(1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{71}{90}\right)\)
\(\chi_{1425}(43,\cdot)\) 1425.ca 36 no \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{1425}(44,\cdot)\) 1425.co 90 yes \(-1\) \(1\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{37}{90}\right)\)
\(\chi_{1425}(46,\cdot)\) 1425.bv 30 no \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1425}(47,\cdot)\) 1425.cr 180 yes \(1\) \(1\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{41}{180}\right)\)
\(\chi_{1425}(49,\cdot)\) 1425.s 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1425}(52,\cdot)\) 1425.cs 180 no \(1\) \(1\) \(e\left(\frac{79}{180}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{97}{180}\right)\) \(e\left(\frac{163}{180}\right)\)
\(\chi_{1425}(53,\cdot)\) 1425.cq 180 yes \(-1\) \(1\) \(e\left(\frac{83}{180}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{29}{180}\right)\) \(e\left(\frac{161}{180}\right)\)
\(\chi_{1425}(56,\cdot)\) 1425.y 10 yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1425}(58,\cdot)\) 1425.bq 20 no \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{1425}(59,\cdot)\) 1425.cm 90 yes \(1\) \(1\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{28}{45}\right)\)
\(\chi_{1425}(61,\cdot)\) 1425.ce 45 no \(1\) \(1\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{2}{45}\right)\)
\(\chi_{1425}(62,\cdot)\) 1425.cr 180 yes \(1\) \(1\) \(e\left(\frac{151}{180}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{37}{180}\right)\)
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