Dirichlet character orbit 3888.ce

• Label: 3888.ce
• Modulus: $3888$
• Conductor: $3888$
• Order: $324$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3888$
Conductor:	$3888$
Order:	$324$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{324})$
Fixed field:	Number field defined by a degree 324 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{3888}(13,\cdot)$	$1$	$1$	$e\left(\frac{287}{324}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{235}{324}\right)$	$e\left(\frac{209}{324}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{80}{81}\right)$
$\chi_{3888}(61,\cdot)$	$1$	$1$	$e\left(\frac{151}{324}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{83}{324}\right)$	$e\left(\frac{49}{324}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{257}{324}\right)$	$e\left(\frac{61}{81}\right)$
$\chi_{3888}(85,\cdot)$	$1$	$1$	$e\left(\frac{65}{324}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{175}{324}\right)$	$e\left(\frac{74}{81}\right)$
$\chi_{3888}(133,\cdot)$	$1$	$1$	$e\left(\frac{109}{324}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{17}{324}\right)$	$e\left(\frac{295}{324}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{119}{324}\right)$	$e\left(\frac{73}{81}\right)$
$\chi_{3888}(157,\cdot)$	$1$	$1$	$e\left(\frac{275}{324}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{31}{324}\right)$	$e\left(\frac{233}{324}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{217}{324}\right)$	$e\left(\frac{14}{81}\right)$
$\chi_{3888}(205,\cdot)$	$1$	$1$	$e\left(\frac{175}{324}\right)$	$e\left(\frac{55}{162}\right)$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{197}{324}\right)$	$e\left(\frac{31}{81}\right)$
$\chi_{3888}(229,\cdot)$	$1$	$1$	$e\left(\frac{269}{324}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{253}{324}\right)$	$e\left(\frac{83}{324}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{79}{162}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{151}{324}\right)$	$e\left(\frac{62}{81}\right)$
$\chi_{3888}(277,\cdot)$	$1$	$1$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{209}{324}\right)$	$e\left(\frac{139}{324}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{16}{81}\right)$
$\chi_{3888}(301,\cdot)$	$1$	$1$	$e\left(\frac{47}{324}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{43}{324}\right)$	$e\left(\frac{41}{324}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{301}{324}\right)$	$e\left(\frac{56}{81}\right)$
$\chi_{3888}(349,\cdot)$	$1$	$1$	$e\left(\frac{307}{324}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{143}{324}\right)$	$e\left(\frac{61}{324}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{101}{162}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{28}{81}\right)$
$\chi_{3888}(373,\cdot)$	$1$	$1$	$e\left(\frac{257}{324}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{49}{324}\right)$	$e\left(\frac{107}{324}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{55}{162}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{19}{324}\right)$	$e\left(\frac{77}{81}\right)$
$\chi_{3888}(421,\cdot)$	$1$	$1$	$e\left(\frac{49}{324}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{293}{324}\right)$	$e\left(\frac{91}{324}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{107}{324}\right)$	$e\left(\frac{67}{81}\right)$
$\chi_{3888}(445,\cdot)$	$1$	$1$	$e\left(\frac{251}{324}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{281}{324}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{277}{324}\right)$	$e\left(\frac{44}{81}\right)$
$\chi_{3888}(493,\cdot)$	$1$	$1$	$e\left(\frac{223}{324}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{11}{324}\right)$	$e\left(\frac{229}{324}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{77}{324}\right)$	$e\left(\frac{52}{81}\right)$
$\chi_{3888}(517,\cdot)$	$1$	$1$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{61}{324}\right)$	$e\left(\frac{239}{324}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{103}{324}\right)$	$e\left(\frac{38}{81}\right)$
$\chi_{3888}(565,\cdot)$	$1$	$1$	$e\left(\frac{181}{324}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{269}{324}\right)$	$e\left(\frac{151}{324}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{263}{324}\right)$	$e\left(\frac{64}{81}\right)$
$\chi_{3888}(589,\cdot)$	$1$	$1$	$e\left(\frac{239}{324}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{67}{324}\right)$	$e\left(\frac{305}{324}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{145}{324}\right)$	$e\left(\frac{59}{81}\right)$
$\chi_{3888}(637,\cdot)$	$1$	$1$	$e\left(\frac{247}{324}\right)$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{95}{324}\right)$	$e\left(\frac{181}{324}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{17}{324}\right)$	$e\left(\frac{22}{81}\right)$
$\chi_{3888}(661,\cdot)$	$1$	$1$	$e\left(\frac{233}{324}\right)$	$e\left(\frac{101}{162}\right)$	$e\left(\frac{289}{324}\right)$	$e\left(\frac{155}{324}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{79}{324}\right)$	$e\left(\frac{26}{81}\right)$
$\chi_{3888}(709,\cdot)$	$1$	$1$	$e\left(\frac{97}{324}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{137}{324}\right)$	$e\left(\frac{319}{324}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{311}{324}\right)$	$e\left(\frac{7}{81}\right)$
$\chi_{3888}(733,\cdot)$	$1$	$1$	$e\left(\frac{11}{324}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{79}{324}\right)$	$e\left(\frac{113}{324}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{229}{324}\right)$	$e\left(\frac{20}{81}\right)$
$\chi_{3888}(781,\cdot)$	$1$	$1$	$e\left(\frac{55}{324}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{71}{324}\right)$	$e\left(\frac{241}{324}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{55}{162}\right)$	$e\left(\frac{173}{324}\right)$	$e\left(\frac{19}{81}\right)$
$\chi_{3888}(805,\cdot)$	$1$	$1$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{85}{324}\right)$	$e\left(\frac{179}{324}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{41}{81}\right)$
$\chi_{3888}(853,\cdot)$	$1$	$1$	$e\left(\frac{121}{324}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{251}{324}\right)$	$e\left(\frac{58}{81}\right)$
$\chi_{3888}(877,\cdot)$	$1$	$1$	$e\left(\frac{215}{324}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{307}{324}\right)$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{205}{324}\right)$	$e\left(\frac{8}{81}\right)$
$\chi_{3888}(925,\cdot)$	$1$	$1$	$e\left(\frac{295}{324}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{263}{324}\right)$	$e\left(\frac{85}{324}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{43}{81}\right)$
$\chi_{3888}(949,\cdot)$	$1$	$1$	$e\left(\frac{317}{324}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{97}{324}\right)$	$e\left(\frac{311}{324}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{31}{324}\right)$	$e\left(\frac{2}{81}\right)$
$\chi_{3888}(997,\cdot)$	$1$	$1$	$e\left(\frac{253}{324}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{197}{324}\right)$	$e\left(\frac{7}{324}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{83}{324}\right)$	$e\left(\frac{55}{81}\right)$
$\chi_{3888}(1021,\cdot)$	$1$	$1$	$e\left(\frac{203}{324}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{103}{324}\right)$	$e\left(\frac{53}{324}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{41}{162}\right)$	$e\left(\frac{73}{324}\right)$	$e\left(\frac{23}{81}\right)$
$\chi_{3888}(1069,\cdot)$	$1$	$1$	$e\left(\frac{319}{324}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{23}{324}\right)$	$e\left(\frac{37}{324}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{161}{324}\right)$	$e\left(\frac{13}{81}\right)$
$\chi_{3888}(1093,\cdot)$	$1$	$1$	$e\left(\frac{197}{324}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{227}{324}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{7}{324}\right)$	$e\left(\frac{71}{81}\right)$