Properties

Modulus $384$
Structure \(C_{32}\times C_{2}\times C_{2}\)
Order $128$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(384)
 
pari: g = idealstar(,384,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 128
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{32}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{384}(127,\cdot)$, $\chi_{384}(133,\cdot)$, $\chi_{384}(257,\cdot)$

First 32 of 128 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{384}(1,\cdot)\) 384.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{384}(5,\cdot)\) 384.x 32 yes \(-1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(i\)
\(\chi_{384}(7,\cdot)\) 384.t 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{384}(11,\cdot)\) 384.w 32 yes \(1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(-i\)
\(\chi_{384}(13,\cdot)\) 384.v 32 no \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(-i\)
\(\chi_{384}(17,\cdot)\) 384.p 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{384}(19,\cdot)\) 384.u 32 no \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(i\)
\(\chi_{384}(23,\cdot)\) 384.s 16 no \(1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(1\)
\(\chi_{384}(25,\cdot)\) 384.r 16 no \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{384}(29,\cdot)\) 384.x 32 yes \(-1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(-i\)
\(\chi_{384}(31,\cdot)\) 384.l 4 no \(-1\) \(1\) \(i\) \(1\) \(-i\) \(-i\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-1\)
\(\chi_{384}(35,\cdot)\) 384.w 32 yes \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(i\)
\(\chi_{384}(37,\cdot)\) 384.v 32 no \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(i\)
\(\chi_{384}(41,\cdot)\) 384.q 16 no \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{384}(43,\cdot)\) 384.u 32 no \(-1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(-i\)
\(\chi_{384}(47,\cdot)\) 384.o 8 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\)
\(\chi_{384}(49,\cdot)\) 384.n 8 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{384}(53,\cdot)\) 384.x 32 yes \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(i\)
\(\chi_{384}(55,\cdot)\) 384.t 16 no \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\)
\(\chi_{384}(59,\cdot)\) 384.w 32 yes \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(-i\)
\(\chi_{384}(61,\cdot)\) 384.v 32 no \(1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(-i\)
\(\chi_{384}(65,\cdot)\) 384.h 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{384}(67,\cdot)\) 384.u 32 no \(-1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(i\)
\(\chi_{384}(71,\cdot)\) 384.s 16 no \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{384}(73,\cdot)\) 384.r 16 no \(1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{384}(77,\cdot)\) 384.x 32 yes \(-1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(-i\)
\(\chi_{384}(79,\cdot)\) 384.m 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\)
\(\chi_{384}(83,\cdot)\) 384.w 32 yes \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(i\)
\(\chi_{384}(85,\cdot)\) 384.v 32 no \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(i\)
\(\chi_{384}(89,\cdot)\) 384.q 16 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{384}(91,\cdot)\) 384.u 32 no \(-1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(-i\)
\(\chi_{384}(95,\cdot)\) 384.k 4 no \(1\) \(1\) \(i\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(-1\) \(-1\) \(-i\) \(-1\)