Properties

Modulus $344$
Structure \(C_{42}\times C_{2}\times C_{2}\)
Order $168$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(344)
 
pari: g = idealstar(,344,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 168
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{42}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{344}(87,\cdot)$, $\chi_{344}(173,\cdot)$, $\chi_{344}(89,\cdot)$

First 32 of 168 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{344}(1,\cdot)\) 344.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{344}(3,\cdot)\) 344.bb 42 yes \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(5,\cdot)\) 344.bf 42 yes \(-1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(7,\cdot)\) 344.k 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{344}(9,\cdot)\) 344.y 21 no \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(11,\cdot)\) 344.s 14 yes \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{344}(13,\cdot)\) 344.z 42 yes \(1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(15,\cdot)\) 344.bc 42 no \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(17,\cdot)\) 344.y 21 no \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{344}(19,\cdot)\) 344.bb 42 yes \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{344}(21,\cdot)\) 344.x 14 yes \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(23,\cdot)\) 344.bc 42 no \(-1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(25,\cdot)\) 344.y 21 no \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{344}(27,\cdot)\) 344.v 14 yes \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(29,\cdot)\) 344.bf 42 yes \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{344}(31,\cdot)\) 344.bc 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(33,\cdot)\) 344.ba 42 no \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{344}(35,\cdot)\) 344.s 14 yes \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(37,\cdot)\) 344.j 6 yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{344}(39,\cdot)\) 344.t 14 no \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(41,\cdot)\) 344.q 7 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(45,\cdot)\) 344.r 14 yes \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{344}(47,\cdot)\) 344.u 14 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{344}(49,\cdot)\) 344.i 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{344}(51,\cdot)\) 344.v 14 yes \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{344}(53,\cdot)\) 344.z 42 yes \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(55,\cdot)\) 344.bd 42 no \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(57,\cdot)\) 344.y 21 no \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{344}(59,\cdot)\) 344.s 14 yes \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{344}(61,\cdot)\) 344.bf 42 yes \(-1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{344}(63,\cdot)\) 344.bd 42 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{344}(65,\cdot)\) 344.w 14 no \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\)