Dirichlet character orbit 8788.be

• Label: 8788.be
• Modulus: $8788$
• Conductor: $2197$
• Order: $676$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$8788$
Conductor:	$2197$
Order:	$676$
Real:	no
Primitive:	no, induced from 2197.p
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{676})$
Fixed field:	Number field defined by a degree 676 polynomial (not computed)

First 31 of 312 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{8788}(5,\cdot)$	$-1$	$1$	$e\left(\frac{93}{169}\right)$	$e\left(\frac{651}{676}\right)$	$e\left(\frac{373}{676}\right)$	$e\left(\frac{17}{169}\right)$	$e\left(\frac{309}{676}\right)$	$e\left(\frac{347}{676}\right)$	$e\left(\frac{297}{338}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{69}{676}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8788}(21,\cdot)$	$-1$	$1$	$e\left(\frac{34}{169}\right)$	$e\left(\frac{69}{676}\right)$	$e\left(\frac{647}{676}\right)$	$e\left(\frac{68}{169}\right)$	$e\left(\frac{391}{676}\right)$	$e\left(\frac{205}{676}\right)$	$e\left(\frac{5}{338}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{107}{676}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8788}(57,\cdot)$	$-1$	$1$	$e\left(\frac{68}{169}\right)$	$e\left(\frac{307}{676}\right)$	$e\left(\frac{449}{676}\right)$	$e\left(\frac{136}{169}\right)$	$e\left(\frac{613}{676}\right)$	$e\left(\frac{579}{676}\right)$	$e\left(\frac{179}{338}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{45}{676}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8788}(73,\cdot)$	$-1$	$1$	$e\left(\frac{111}{169}\right)$	$e\left(\frac{101}{676}\right)$	$e\left(\frac{467}{676}\right)$	$e\left(\frac{53}{169}\right)$	$e\left(\frac{347}{676}\right)$	$e\left(\frac{545}{676}\right)$	$e\left(\frac{71}{338}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{235}{676}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8788}(109,\cdot)$	$-1$	$1$	$e\left(\frac{134}{169}\right)$	$e\left(\frac{431}{676}\right)$	$e\left(\frac{5}{676}\right)$	$e\left(\frac{99}{169}\right)$	$e\left(\frac{189}{676}\right)$	$e\left(\frac{291}{676}\right)$	$e\left(\frac{139}{338}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{541}{676}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8788}(125,\cdot)$	$-1$	$1$	$e\left(\frac{110}{169}\right)$	$e\left(\frac{601}{676}\right)$	$e\left(\frac{443}{676}\right)$	$e\left(\frac{51}{169}\right)$	$e\left(\frac{251}{676}\right)$	$e\left(\frac{365}{676}\right)$	$e\left(\frac{215}{338}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{207}{676}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8788}(161,\cdot)$	$-1$	$1$	$e\left(\frac{122}{169}\right)$	$e\left(\frac{347}{676}\right)$	$e\left(\frac{393}{676}\right)$	$e\left(\frac{75}{169}\right)$	$e\left(\frac{389}{676}\right)$	$e\left(\frac{159}{676}\right)$	$e\left(\frac{177}{338}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{205}{676}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8788}(177,\cdot)$	$-1$	$1$	$e\left(\frac{31}{169}\right)$	$e\left(\frac{217}{676}\right)$	$e\left(\frac{575}{676}\right)$	$e\left(\frac{62}{169}\right)$	$e\left(\frac{103}{676}\right)$	$e\left(\frac{341}{676}\right)$	$e\left(\frac{99}{338}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{23}{676}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{8788}(213,\cdot)$	$-1$	$1$	$e\left(\frac{32}{169}\right)$	$e\left(\frac{55}{676}\right)$	$e\left(\frac{261}{676}\right)$	$e\left(\frac{64}{169}\right)$	$e\left(\frac{537}{676}\right)$	$e\left(\frac{183}{676}\right)$	$e\left(\frac{293}{338}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{389}{676}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8788}(229,\cdot)$	$-1$	$1$	$e\left(\frac{43}{169}\right)$	$e\left(\frac{301}{676}\right)$	$e\left(\frac{187}{676}\right)$	$e\left(\frac{86}{169}\right)$	$e\left(\frac{579}{676}\right)$	$e\left(\frac{473}{676}\right)$	$e\left(\frac{61}{338}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{359}{676}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8788}(265,\cdot)$	$-1$	$1$	$e\left(\frac{33}{169}\right)$	$e\left(\frac{231}{676}\right)$	$e\left(\frac{285}{676}\right)$	$e\left(\frac{66}{169}\right)$	$e\left(\frac{633}{676}\right)$	$e\left(\frac{363}{676}\right)$	$e\left(\frac{149}{338}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{417}{676}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8788}(281,\cdot)$	$-1$	$1$	$e\left(\frac{146}{169}\right)$	$e\left(\frac{177}{676}\right)$	$e\left(\frac{631}{676}\right)$	$e\left(\frac{123}{169}\right)$	$e\left(\frac{327}{676}\right)$	$e\left(\frac{85}{676}\right)$	$e\left(\frac{101}{338}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{539}{676}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8788}(317,\cdot)$	$-1$	$1$	$e\left(\frac{125}{169}\right)$	$e\left(\frac{199}{676}\right)$	$e\left(\frac{465}{676}\right)$	$e\left(\frac{81}{169}\right)$	$e\left(\frac{1}{676}\right)$	$e\left(\frac{23}{676}\right)$	$e\left(\frac{83}{338}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{289}{676}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8788}(333,\cdot)$	$-1$	$1$	$e\left(\frac{2}{169}\right)$	$e\left(\frac{521}{676}\right)$	$e\left(\frac{555}{676}\right)$	$e\left(\frac{4}{169}\right)$	$e\left(\frac{23}{676}\right)$	$e\left(\frac{529}{676}\right)$	$e\left(\frac{219}{338}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{563}{676}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8788}(369,\cdot)$	$-1$	$1$	$e\left(\frac{139}{169}\right)$	$e\left(\frac{635}{676}\right)$	$e\left(\frac{125}{676}\right)$	$e\left(\frac{109}{169}\right)$	$e\left(\frac{669}{676}\right)$	$e\left(\frac{515}{676}\right)$	$e\left(\frac{95}{338}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{5}{676}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8788}(385,\cdot)$	$-1$	$1$	$e\left(\frac{118}{169}\right)$	$e\left(\frac{657}{676}\right)$	$e\left(\frac{635}{676}\right)$	$e\left(\frac{67}{169}\right)$	$e\left(\frac{343}{676}\right)$	$e\left(\frac{453}{676}\right)$	$e\left(\frac{77}{338}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{431}{676}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8788}(421,\cdot)$	$-1$	$1$	$e\left(\frac{75}{169}\right)$	$e\left(\frac{187}{676}\right)$	$e\left(\frac{617}{676}\right)$	$e\left(\frac{150}{169}\right)$	$e\left(\frac{609}{676}\right)$	$e\left(\frac{487}{676}\right)$	$e\left(\frac{185}{338}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{241}{676}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8788}(473,\cdot)$	$-1$	$1$	$e\left(\frac{102}{169}\right)$	$e\left(\frac{207}{676}\right)$	$e\left(\frac{589}{676}\right)$	$e\left(\frac{35}{169}\right)$	$e\left(\frac{497}{676}\right)$	$e\left(\frac{615}{676}\right)$	$e\left(\frac{15}{338}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{321}{676}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8788}(489,\cdot)$	$-1$	$1$	$e\left(\frac{116}{169}\right)$	$e\left(\frac{305}{676}\right)$	$e\left(\frac{587}{676}\right)$	$e\left(\frac{63}{169}\right)$	$e\left(\frac{151}{676}\right)$	$e\left(\frac{93}{676}\right)$	$e\left(\frac{27}{338}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{375}{676}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8788}(525,\cdot)$	$-1$	$1$	$e\left(\frac{51}{169}\right)$	$e\left(\frac{19}{676}\right)$	$e\left(\frac{41}{676}\right)$	$e\left(\frac{102}{169}\right)$	$e\left(\frac{333}{676}\right)$	$e\left(\frac{223}{676}\right)$	$e\left(\frac{261}{338}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{245}{676}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{8788}(541,\cdot)$	$-1$	$1$	$e\left(\frac{167}{169}\right)$	$e\left(\frac{493}{676}\right)$	$e\left(\frac{459}{676}\right)$	$e\left(\frac{165}{169}\right)$	$e\left(\frac{315}{676}\right)$	$e\left(\frac{485}{676}\right)$	$e\left(\frac{119}{338}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{451}{676}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{8788}(593,\cdot)$	$-1$	$1$	$e\left(\frac{140}{169}\right)$	$e\left(\frac{473}{676}\right)$	$e\left(\frac{487}{676}\right)$	$e\left(\frac{111}{169}\right)$	$e\left(\frac{427}{676}\right)$	$e\left(\frac{357}{676}\right)$	$e\left(\frac{289}{338}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{371}{676}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{8788}(629,\cdot)$	$-1$	$1$	$e\left(\frac{53}{169}\right)$	$e\left(\frac{371}{676}\right)$	$e\left(\frac{89}{676}\right)$	$e\left(\frac{106}{169}\right)$	$e\left(\frac{525}{676}\right)$	$e\left(\frac{583}{676}\right)$	$e\left(\frac{311}{338}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{301}{676}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{8788}(645,\cdot)$	$-1$	$1$	$e\left(\frac{35}{169}\right)$	$e\left(\frac{245}{676}\right)$	$e\left(\frac{671}{676}\right)$	$e\left(\frac{70}{169}\right)$	$e\left(\frac{487}{676}\right)$	$e\left(\frac{385}{676}\right)$	$e\left(\frac{199}{338}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{135}{676}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8788}(681,\cdot)$	$-1$	$1$	$e\left(\frac{106}{169}\right)$	$e\left(\frac{235}{676}\right)$	$e\left(\frac{9}{676}\right)$	$e\left(\frac{43}{169}\right)$	$e\left(\frac{205}{676}\right)$	$e\left(\frac{659}{676}\right)$	$e\left(\frac{115}{338}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{433}{676}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8788}(697,\cdot)$	$-1$	$1$	$e\left(\frac{21}{169}\right)$	$e\left(\frac{485}{676}\right)$	$e\left(\frac{335}{676}\right)$	$e\left(\frac{42}{169}\right)$	$e\left(\frac{495}{676}\right)$	$e\left(\frac{569}{676}\right)$	$e\left(\frac{187}{338}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{419}{676}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8788}(733,\cdot)$	$-1$	$1$	$e\left(\frac{81}{169}\right)$	$e\left(\frac{567}{676}\right)$	$e\left(\frac{85}{676}\right)$	$e\left(\frac{162}{169}\right)$	$e\left(\frac{509}{676}\right)$	$e\left(\frac{215}{676}\right)$	$e\left(\frac{335}{338}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{409}{676}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8788}(749,\cdot)$	$-1$	$1$	$e\left(\frac{98}{169}\right)$	$e\left(\frac{517}{676}\right)$	$e\left(\frac{155}{676}\right)$	$e\left(\frac{27}{169}\right)$	$e\left(\frac{451}{676}\right)$	$e\left(\frac{233}{676}\right)$	$e\left(\frac{253}{338}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{547}{676}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{8788}(785,\cdot)$	$-1$	$1$	$e\left(\frac{147}{169}\right)$	$e\left(\frac{15}{676}\right)$	$e\left(\frac{317}{676}\right)$	$e\left(\frac{125}{169}\right)$	$e\left(\frac{85}{676}\right)$	$e\left(\frac{603}{676}\right)$	$e\left(\frac{295}{338}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{229}{676}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{8788}(801,\cdot)$	$-1$	$1$	$e\left(\frac{97}{169}\right)$	$e\left(\frac{341}{676}\right)$	$e\left(\frac{131}{676}\right)$	$e\left(\frac{25}{169}\right)$	$e\left(\frac{355}{676}\right)$	$e\left(\frac{53}{676}\right)$	$e\left(\frac{59}{338}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{519}{676}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{8788}(837,\cdot)$	$-1$	$1$	$e\left(\frac{135}{169}\right)$	$e\left(\frac{607}{676}\right)$	$e\left(\frac{29}{676}\right)$	$e\left(\frac{101}{169}\right)$	$e\left(\frac{285}{676}\right)$	$e\left(\frac{471}{676}\right)$	$e\left(\frac{333}{338}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{569}{676}\right)$	$e\left(\frac{17}{26}\right)$