# Properties

 Modulus $3584$ Structure $$C_{2}\times C_{2}\times C_{384}$$ Order $1536$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3584)

pari: g = idealstar(,3584,2)

## Character group

 sage: G.order()  pari: g.no Order = 1536 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{384}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3584}(1023,\cdot)$, $\chi_{3584}(1541,\cdot)$, $\chi_{3584}(1025,\cdot)$

## First 32 of 1536 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{3584}(1,\cdot)$$ 3584.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3584}(3,\cdot)$$ 3584.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{91}{384}\right)$$ $$e\left(\frac{41}{384}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{157}{384}\right)$$ $$e\left(\frac{109}{128}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{239}{384}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{41}{192}\right)$$
$$\chi_{3584}(5,\cdot)$$ 3584.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{41}{384}\right)$$ $$e\left(\frac{67}{384}\right)$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{383}{384}\right)$$ $$e\left(\frac{47}{128}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{133}{384}\right)$$ $$e\left(\frac{149}{192}\right)$$ $$e\left(\frac{67}{192}\right)$$
$$\chi_{3584}(9,\cdot)$$ 3584.cf 192 no $$1$$ $$1$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$
$$\chi_{3584}(11,\cdot)$$ 3584.cj 384 yes $$-1$$ $$1$$ $$e\left(\frac{157}{384}\right)$$ $$e\left(\frac{383}{384}\right)$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{235}{384}\right)$$ $$e\left(\frac{91}{128}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{41}{384}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{191}{192}\right)$$
$$\chi_{3584}(13,\cdot)$$ 3584.cd 128 yes $$-1$$ $$1$$ $$e\left(\frac{109}{128}\right)$$ $$e\left(\frac{47}{128}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{91}{128}\right)$$ $$e\left(\frac{97}{128}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{57}{128}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{47}{64}\right)$$
$$\chi_{3584}(15,\cdot)$$ 3584.bl 32 no $$-1$$ $$1$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{3584}(17,\cdot)$$ 3584.bz 96 no $$-1$$ $$1$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{3584}(19,\cdot)$$ 3584.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{239}{384}\right)$$ $$e\left(\frac{133}{384}\right)$$ $$e\left(\frac{47}{192}\right)$$ $$e\left(\frac{41}{384}\right)$$ $$e\left(\frac{57}{128}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{307}{384}\right)$$ $$e\left(\frac{131}{192}\right)$$ $$e\left(\frac{133}{192}\right)$$
$$\chi_{3584}(23,\cdot)$$ 3584.ch 192 no $$-1$$ $$1$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{149}{192}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{131}{192}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{53}{96}\right)$$
$$\chi_{3584}(25,\cdot)$$ 3584.cf 192 no $$1$$ $$1$$ $$e\left(\frac{41}{192}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{67}{96}\right)$$
$$\chi_{3584}(27,\cdot)$$ 3584.cb 128 yes $$1$$ $$1$$ $$e\left(\frac{91}{128}\right)$$ $$e\left(\frac{41}{128}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{29}{128}\right)$$ $$e\left(\frac{71}{128}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{111}{128}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{41}{64}\right)$$
$$\chi_{3584}(29,\cdot)$$ 3584.ca 128 no $$1$$ $$1$$ $$e\left(\frac{81}{128}\right)$$ $$e\left(\frac{123}{128}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{87}{128}\right)$$ $$e\left(\frac{85}{128}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{13}{128}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$
$$\chi_{3584}(31,\cdot)$$ 3584.bq 48 no $$1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{3584}(33,\cdot)$$ 3584.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{3584}(37,\cdot)$$ 3584.cl 384 yes $$1$$ $$1$$ $$e\left(\frac{65}{384}\right)$$ $$e\left(\frac{331}{384}\right)$$ $$e\left(\frac{65}{192}\right)$$ $$e\left(\frac{359}{384}\right)$$ $$e\left(\frac{87}{128}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{61}{384}\right)$$ $$e\left(\frac{77}{192}\right)$$ $$e\left(\frac{139}{192}\right)$$
$$\chi_{3584}(39,\cdot)$$ 3584.ch 192 no $$-1$$ $$1$$ $$e\left(\frac{17}{192}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{23}{192}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{91}{96}\right)$$
$$\chi_{3584}(41,\cdot)$$ 3584.bt 64 no $$-1$$ $$1$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$
$$\chi_{3584}(43,\cdot)$$ 3584.cc 128 no $$-1$$ $$1$$ $$e\left(\frac{23}{128}\right)$$ $$e\left(\frac{61}{128}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{1}{128}\right)$$ $$e\left(\frac{115}{128}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{59}{128}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$
$$\chi_{3584}(45,\cdot)$$ 3584.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{223}{384}\right)$$ $$e\left(\frac{149}{384}\right)$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{313}{384}\right)$$ $$e\left(\frac{9}{128}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{227}{384}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{149}{192}\right)$$
$$\chi_{3584}(47,\cdot)$$ 3584.bx 96 no $$1$$ $$1$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{3584}(51,\cdot)$$ 3584.cj 384 yes $$-1$$ $$1$$ $$e\left(\frac{23}{384}\right)$$ $$e\left(\frac{61}{384}\right)$$ $$e\left(\frac{23}{192}\right)$$ $$e\left(\frac{257}{384}\right)$$ $$e\left(\frac{81}{128}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{187}{384}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{61}{192}\right)$$
$$\chi_{3584}(53,\cdot)$$ 3584.cl 384 yes $$1$$ $$1$$ $$e\left(\frac{13}{384}\right)$$ $$e\left(\frac{143}{384}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{379}{384}\right)$$ $$e\left(\frac{43}{128}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{89}{384}\right)$$ $$e\left(\frac{169}{192}\right)$$ $$e\left(\frac{143}{192}\right)$$
$$\chi_{3584}(55,\cdot)$$ 3584.bv 64 no $$1$$ $$1$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{3584}(57,\cdot)$$ 3584.bs 64 no $$1$$ $$1$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$
$$\chi_{3584}(59,\cdot)$$ 3584.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{313}{384}\right)$$ $$e\left(\frac{179}{384}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{367}{384}\right)$$ $$e\left(\frac{95}{128}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{341}{384}\right)$$ $$e\left(\frac{133}{192}\right)$$ $$e\left(\frac{179}{192}\right)$$
$$\chi_{3584}(61,\cdot)$$ 3584.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{203}{384}\right)$$ $$e\left(\frac{313}{384}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{173}{384}\right)$$ $$e\left(\frac{61}{128}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{31}{384}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{121}{192}\right)$$
$$\chi_{3584}(65,\cdot)$$ 3584.bh 24 no $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{3584}(67,\cdot)$$ 3584.cj 384 yes $$-1$$ $$1$$ $$e\left(\frac{235}{384}\right)$$ $$e\left(\frac{89}{384}\right)$$ $$e\left(\frac{43}{192}\right)$$ $$e\left(\frac{205}{384}\right)$$ $$e\left(\frac{93}{128}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{191}{384}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{89}{192}\right)$$
$$\chi_{3584}(69,\cdot)$$ 3584.cd 128 yes $$-1$$ $$1$$ $$e\left(\frac{115}{128}\right)$$ $$e\left(\frac{113}{128}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{69}{128}\right)$$ $$e\left(\frac{127}{128}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{39}{128}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$
$$\chi_{3584}(71,\cdot)$$ 3584.bu 64 no $$-1$$ $$1$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{3584}(73,\cdot)$$ 3584.ce 192 no $$-1$$ $$1$$ $$e\left(\frac{179}{192}\right)$$ $$e\left(\frac{49}{192}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$