Properties

Modulus $143$
Structure \(C_{2}\times C_{60}\)
Order $120$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(143)
 
pari: g = idealstar(,143,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 120
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{143}(79,\cdot)$, $\chi_{143}(67,\cdot)$

First 32 of 120 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{143}(1,\cdot)\) 143.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{143}(2,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{143}(3,\cdot)\) 143.q 15 yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{143}(4,\cdot)\) 143.u 30 yes \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{143}(5,\cdot)\) 143.r 20 yes \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(6,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{143}(7,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{143}(8,\cdot)\) 143.s 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(-1\)
\(\chi_{143}(9,\cdot)\) 143.q 15 yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{143}(10,\cdot)\) 143.i 6 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{143}(12,\cdot)\) 143.b 2 no \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{143}(14,\cdot)\) 143.h 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)
\(\chi_{143}(15,\cdot)\) 143.x 60 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)
\(\chi_{143}(16,\cdot)\) 143.q 15 yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{143}(17,\cdot)\) 143.v 30 yes \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(18,\cdot)\) 143.s 20 yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(-1\)
\(\chi_{143}(19,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{143}(20,\cdot)\) 143.x 60 yes \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)
\(\chi_{143}(21,\cdot)\) 143.g 4 yes \(1\) \(1\) \(-i\) \(1\) \(-1\) \(i\) \(-i\) \(i\) \(i\) \(1\) \(1\) \(-1\)
\(\chi_{143}(23,\cdot)\) 143.j 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{143}(24,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{143}(25,\cdot)\) 143.n 10 yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)
\(\chi_{143}(27,\cdot)\) 143.h 5 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)
\(\chi_{143}(28,\cdot)\) 143.w 60 yes \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{143}(29,\cdot)\) 143.t 30 yes \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{143}(30,\cdot)\) 143.v 30 yes \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(31,\cdot)\) 143.r 20 yes \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(-1\)
\(\chi_{143}(32,\cdot)\) 143.o 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{143}(34,\cdot)\) 143.f 4 no \(-1\) \(1\) \(i\) \(1\) \(-1\) \(i\) \(i\) \(-i\) \(-i\) \(1\) \(-1\) \(-1\)
\(\chi_{143}(35,\cdot)\) 143.t 30 yes \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{143}(36,\cdot)\) 143.u 30 yes \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{143}(37,\cdot)\) 143.x 60 yes \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)
Click here to search among the remaining 88 characters.