Dirichlet character orbit 759.z

• Label: 759.z
• Modulus: $759$
• Conductor: $253$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$759$
Conductor:	$253$
Order:	$110$
Real:	no
Primitive:	no, induced from 253.n
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{759}(7,\cdot)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{759}(19,\cdot)$	$1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{759}(28,\cdot)$	$1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{759}(40,\cdot)$	$1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{759}(61,\cdot)$	$1$	$1$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{759}(79,\cdot)$	$1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{759}(106,\cdot)$	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{759}(112,\cdot)$	$1$	$1$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{759}(145,\cdot)$	$1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{759}(172,\cdot)$	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{759}(178,\cdot)$	$1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{759}(205,\cdot)$	$1$	$1$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{759}(217,\cdot)$	$1$	$1$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{759}(226,\cdot)$	$1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{759}(244,\cdot)$	$1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{759}(250,\cdot)$	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{759}(283,\cdot)$	$1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{759}(304,\cdot)$	$1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{759}(310,\cdot)$	$1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{759}(316,\cdot)$	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{759}(337,\cdot)$	$1$	$1$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{759}(343,\cdot)$	$1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{759}(382,\cdot)$	$1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{759}(424,\cdot)$	$1$	$1$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{759}(442,\cdot)$	$1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{759}(448,\cdot)$	$1$	$1$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{759}(457,\cdot)$	$1$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{759}(475,\cdot)$	$1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{759}(481,\cdot)$	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{759}(490,\cdot)$	$1$	$1$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{759}(502,\cdot)$	$1$	$1$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{4}{55}\right)$