Properties

Modulus $675$
Structure \(C_{2}\times C_{180}\)
Order $360$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(675)
 
pari: g = idealstar(,675,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 360
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{180}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{675}(326,\cdot)$, $\chi_{675}(352,\cdot)$

First 32 of 360 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{675}(1,\cdot)\) 675.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{675}(2,\cdot)\) 675.bi 180 yes \(1\) \(1\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{675}(4,\cdot)\) 675.bg 90 yes \(1\) \(1\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{675}(7,\cdot)\) 675.bb 36 no \(-1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{675}(8,\cdot)\) 675.bd 60 no \(1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{675}(11,\cdot)\) 675.bf 90 yes \(-1\) \(1\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{675}(13,\cdot)\) 675.bj 180 yes \(-1\) \(1\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{675}(14,\cdot)\) 675.bh 90 yes \(-1\) \(1\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{675}(16,\cdot)\) 675.bc 45 yes \(1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{675}(17,\cdot)\) 675.bd 60 no \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{675}(19,\cdot)\) 675.y 30 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(22,\cdot)\) 675.bj 180 yes \(-1\) \(1\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{675}(23,\cdot)\) 675.bi 180 yes \(1\) \(1\) \(e\left(\frac{29}{180}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{675}(26,\cdot)\) 675.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{675}(28,\cdot)\) 675.v 20 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{675}(29,\cdot)\) 675.bh 90 yes \(-1\) \(1\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{675}(31,\cdot)\) 675.bc 45 yes \(1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{675}(32,\cdot)\) 675.ba 36 no \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{675}(34,\cdot)\) 675.bg 90 yes \(1\) \(1\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{675}(37,\cdot)\) 675.be 60 no \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{675}(38,\cdot)\) 675.bi 180 yes \(1\) \(1\) \(e\left(\frac{121}{180}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{149}{180}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{675}(41,\cdot)\) 675.bf 90 yes \(-1\) \(1\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{675}(43,\cdot)\) 675.bb 36 no \(-1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{675}(44,\cdot)\) 675.z 30 no \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(46,\cdot)\) 675.r 15 no \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{675}(47,\cdot)\) 675.bi 180 yes \(1\) \(1\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{675}(49,\cdot)\) 675.u 18 no \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{675}(52,\cdot)\) 675.bj 180 yes \(-1\) \(1\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{675}(53,\cdot)\) 675.w 20 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{675}(56,\cdot)\) 675.bf 90 yes \(-1\) \(1\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{675}(58,\cdot)\) 675.bj 180 yes \(-1\) \(1\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{675}(59,\cdot)\) 675.bh 90 yes \(-1\) \(1\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
Click here to search among the remaining 328 characters.