# Properties

 Modulus $4608$ Structure $$C_{2}\times C_{2}\times C_{384}$$ Order $1536$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4608)

pari: g = idealstar(,4608,2)

## 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 = $\chi_{4608}(3583,\cdot)$, $\chi_{4608}(2053,\cdot)$, $\chi_{4608}(4097,\cdot)$

## 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{4608}(1,\cdot)$$ 4608.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4608}(5,\cdot)$$ 4608.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{67}{384}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{191}{384}\right)$$ $$e\left(\frac{205}{384}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{23}{128}\right)$$ $$e\left(\frac{53}{192}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{305}{384}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{4608}(7,\cdot)$$ 4608.cg 192 no $$-1$$ $$1$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{59}{192}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{149}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{4608}(11,\cdot)$$ 4608.cj 384 yes $$1$$ $$1$$ $$e\left(\frac{191}{384}\right)$$ $$e\left(\frac{59}{192}\right)$$ $$e\left(\frac{43}{384}\right)$$ $$e\left(\frac{17}{384}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{99}{128}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{325}{384}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{4608}(13,\cdot)$$ 4608.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{205}{384}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{17}{384}\right)$$ $$e\left(\frac{355}{384}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{121}{128}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{383}{384}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{4608}(17,\cdot)$$ 4608.bn 32 no $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$-i$$
$$\chi_{4608}(19,\cdot)$$ 4608.ca 128 no $$-1$$ $$1$$ $$e\left(\frac{23}{128}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{99}{128}\right)$$ $$e\left(\frac{121}{128}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{81}{128}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{13}{128}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{4608}(23,\cdot)$$ 4608.ch 192 no $$1$$ $$1$$ $$e\left(\frac{53}{192}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{121}{192}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{1}{24}\right)$$
$$\chi_{4608}(25,\cdot)$$ 4608.ce 192 no $$1$$ $$1$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{13}{192}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{113}{192}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{4608}(29,\cdot)$$ 4608.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{305}{384}\right)$$ $$e\left(\frac{149}{192}\right)$$ $$e\left(\frac{325}{384}\right)$$ $$e\left(\frac{383}{384}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{128}\right)$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{113}{192}\right)$$ $$e\left(\frac{139}{384}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{4608}(31,\cdot)$$ 4608.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4608}(35,\cdot)$$ 4608.cc 128 no $$1$$ $$1$$ $$e\left(\frac{11}{128}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{103}{128}\right)$$ $$e\left(\frac{5}{128}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{125}{128}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{73}{128}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{4608}(37,\cdot)$$ 4608.cb 128 no $$1$$ $$1$$ $$e\left(\frac{25}{128}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{77}{128}\right)$$ $$e\left(\frac{87}{128}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{63}{128}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{3}{128}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{4608}(41,\cdot)$$ 4608.cf 192 no $$-1$$ $$1$$ $$e\left(\frac{29}{192}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{179}{192}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{4608}(43,\cdot)$$ 4608.cl 384 yes $$-1$$ $$1$$ $$e\left(\frac{311}{384}\right)$$ $$e\left(\frac{83}{192}\right)$$ $$e\left(\frac{259}{384}\right)$$ $$e\left(\frac{89}{384}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{59}{128}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{119}{192}\right)$$ $$e\left(\frac{109}{384}\right)$$ $$e\left(\frac{31}{48}\right)$$
$$\chi_{4608}(47,\cdot)$$ 4608.bw 96 no $$1$$ $$1$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4608}(49,\cdot)$$ 4608.bz 96 no $$1$$ $$1$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4608}(53,\cdot)$$ 4608.cd 128 no $$-1$$ $$1$$ $$e\left(\frac{69}{128}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{105}{128}\right)$$ $$e\left(\frac{43}{128}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{115}{128}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{39}{128}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{4608}(55,\cdot)$$ 4608.bv 64 no $$-1$$ $$1$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{4608}(59,\cdot)$$ 4608.cj 384 yes $$1$$ $$1$$ $$e\left(\frac{307}{384}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{47}{384}\right)$$ $$e\left(\frac{349}{384}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{7}{128}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{257}{384}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{4608}(61,\cdot)$$ 4608.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{377}{384}\right)$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{301}{384}\right)$$ $$e\left(\frac{119}{384}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{117}{128}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{163}{384}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{4608}(65,\cdot)$$ 4608.bi 24 no $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4608}(67,\cdot)$$ 4608.cl 384 yes $$-1$$ $$1$$ $$e\left(\frac{217}{384}\right)$$ $$e\left(\frac{61}{192}\right)$$ $$e\left(\frac{77}{384}\right)$$ $$e\left(\frac{151}{384}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{21}{128}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{323}{384}\right)$$ $$e\left(\frac{17}{48}\right)$$
$$\chi_{4608}(71,\cdot)$$ 4608.bu 64 no $$1$$ $$1$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{4608}(73,\cdot)$$ 4608.bt 64 no $$1$$ $$1$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{4608}(77,\cdot)$$ 4608.ci 384 yes $$-1$$ $$1$$ $$e\left(\frac{157}{384}\right)$$ $$e\left(\frac{49}{192}\right)$$ $$e\left(\frac{161}{384}\right)$$ $$e\left(\frac{211}{384}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{73}{128}\right)$$ $$e\left(\frac{107}{192}\right)$$ $$e\left(\frac{157}{192}\right)$$ $$e\left(\frac{239}{384}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{4608}(79,\cdot)$$ 4608.by 96 no $$-1$$ $$1$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4608}(83,\cdot)$$ 4608.cj 384 yes $$1$$ $$1$$ $$e\left(\frac{245}{384}\right)$$ $$e\left(\frac{137}{192}\right)$$ $$e\left(\frac{25}{384}\right)$$ $$e\left(\frac{251}{384}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{1}{128}\right)$$ $$e\left(\frac{115}{192}\right)$$ $$e\left(\frac{53}{192}\right)$$ $$e\left(\frac{55}{384}\right)$$ $$e\left(\frac{13}{48}\right)$$
$$\chi_{4608}(85,\cdot)$$ 4608.ck 384 yes $$1$$ $$1$$ $$e\left(\frac{343}{384}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{227}{384}\right)$$ $$e\left(\frac{313}{384}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{27}{128}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{151}{192}\right)$$ $$e\left(\frac{77}{384}\right)$$ $$e\left(\frac{23}{48}\right)$$
$$\chi_{4608}(89,\cdot)$$ 4608.bs 64 no $$-1$$ $$1$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{4608}(91,\cdot)$$ 4608.ca 128 no $$-1$$ $$1$$ $$e\left(\frac{57}{128}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{45}{128}\right)$$ $$e\left(\frac{55}{128}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{95}{128}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{99}{128}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{4608}(95,\cdot)$$ 4608.bp 48 no $$1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$