Dirichlet character orbit 512.o

• Label: 512.o
• Modulus: $512$
• Conductor: $512$
• Order: $128$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$512$
Conductor:	$512$
Order:	$128$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{128})$
Fixed field:	Number field defined by a degree 128 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{512}(5,\cdot)$	$1$	$1$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{109}{128}\right)$
$\chi_{512}(13,\cdot)$	$1$	$1$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{67}{128}\right)$
$\chi_{512}(21,\cdot)$	$1$	$1$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{105}{128}\right)$
$\chi_{512}(29,\cdot)$	$1$	$1$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{95}{128}\right)$
$\chi_{512}(37,\cdot)$	$1$	$1$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{37}{128}\right)$
$\chi_{512}(45,\cdot)$	$1$	$1$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{19}{128}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{59}{128}\right)$
$\chi_{512}(53,\cdot)$	$1$	$1$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{33}{128}\right)$
$\chi_{512}(61,\cdot)$	$1$	$1$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{87}{128}\right)$
$\chi_{512}(69,\cdot)$	$1$	$1$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{93}{128}\right)$
$\chi_{512}(77,\cdot)$	$1$	$1$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{31}{128}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{51}{128}\right)$
$\chi_{512}(85,\cdot)$	$1$	$1$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{19}{128}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{89}{128}\right)$
$\chi_{512}(93,\cdot)$	$1$	$1$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{79}{128}\right)$
$\chi_{512}(101,\cdot)$	$1$	$1$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{21}{128}\right)$
$\chi_{512}(109,\cdot)$	$1$	$1$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{43}{128}\right)$
$\chi_{512}(117,\cdot)$	$1$	$1$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{17}{128}\right)$
$\chi_{512}(125,\cdot)$	$1$	$1$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{71}{128}\right)$
$\chi_{512}(133,\cdot)$	$1$	$1$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{77}{128}\right)$
$\chi_{512}(141,\cdot)$	$1$	$1$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{79}{128}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{35}{128}\right)$
$\chi_{512}(149,\cdot)$	$1$	$1$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{73}{128}\right)$
$\chi_{512}(157,\cdot)$	$1$	$1$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{63}{128}\right)$
$\chi_{512}(165,\cdot)$	$1$	$1$	$e\left(\frac{11}{128}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{5}{128}\right)$
$\chi_{512}(173,\cdot)$	$1$	$1$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{27}{128}\right)$
$\chi_{512}(181,\cdot)$	$1$	$1$	$e\left(\frac{79}{128}\right)$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{19}{128}\right)$	$e\left(\frac{1}{128}\right)$
$\chi_{512}(189,\cdot)$	$1$	$1$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{55}{128}\right)$
$\chi_{512}(197,\cdot)$	$1$	$1$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{61}{128}\right)$
$\chi_{512}(205,\cdot)$	$1$	$1$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{19}{128}\right)$
$\chi_{512}(213,\cdot)$	$1$	$1$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{57}{128}\right)$
$\chi_{512}(221,\cdot)$	$1$	$1$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{11}{128}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{47}{128}\right)$
$\chi_{512}(229,\cdot)$	$1$	$1$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{117}{128}\right)$
$\chi_{512}(237,\cdot)$	$1$	$1$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{11}{128}\right)$
$\chi_{512}(245,\cdot)$	$1$	$1$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{113}{128}\right)$