Properties

Modulus $407$
Structure \(C_{180}\times C_{2}\)
Order $360$

Learn more

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(407)
 
pari: g = idealstar(,407,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 360
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{180}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{407}(112,\cdot)$, $\chi_{407}(298,\cdot)$

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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{407}(1,\cdot)\) 407.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{407}(2,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{7}{180}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(3,\cdot)\) 407.bg 90 yes \(1\) \(1\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(4,\cdot)\) 407.bg 90 yes \(1\) \(1\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(5,\cdot)\) 407.bi 180 yes \(-1\) \(1\) \(e\left(\frac{7}{180}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{53}{180}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(6,\cdot)\) 407.w 20 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(1\)
\(\chi_{407}(7,\cdot)\) 407.bh 90 yes \(-1\) \(1\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(8,\cdot)\) 407.bd 60 yes \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(9,\cdot)\) 407.bc 45 yes \(1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(10,\cdot)\) 407.j 6 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(12,\cdot)\) 407.l 9 no \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(13,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{73}{180}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(14,\cdot)\) 407.be 60 yes \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(15,\cdot)\) 407.bi 180 yes \(-1\) \(1\) \(e\left(\frac{101}{180}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(16,\cdot)\) 407.bc 45 yes \(1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(17,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{17}{180}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(18,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{31}{180}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(19,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{101}{180}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(20,\cdot)\) 407.bi 180 yes \(-1\) \(1\) \(e\left(\frac{53}{180}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(21,\cdot)\) 407.u 18 yes \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(23,\cdot)\) 407.p 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(24,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{167}{180}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(25,\cdot)\) 407.bg 90 yes \(1\) \(1\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(26,\cdot)\) 407.r 15 yes \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(27,\cdot)\) 407.x 30 yes \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(28,\cdot)\) 407.bf 90 yes \(-1\) \(1\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(29,\cdot)\) 407.bd 60 yes \(1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(30,\cdot)\) 407.bf 90 yes \(-1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(31,\cdot)\) 407.v 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)
\(\chi_{407}(32,\cdot)\) 407.bb 36 yes \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(34,\cdot)\) 407.l 9 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(35,\cdot)\) 407.bj 180 yes \(1\) \(1\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{97}{180}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\)