Dirichlet character orbit 484.o

• Label: 484.o
• Modulus: $484$
• Conductor: $484$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$484$
Conductor:	$484$
Order:	$110$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{484}(15,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{484}(31,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{484}(47,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{484}(59,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{484}(71,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{484}(75,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{484}(91,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{484}(103,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{484}(115,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{484}(119,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{484}(135,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{484}(147,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{484}(159,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{484}(163,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{484}(179,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{484}(191,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{484}(203,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{484}(207,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{484}(223,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{484}(235,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{484}(247,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{484}(267,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{484}(279,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{484}(291,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{484}(295,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{484}(311,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{484}(335,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{484}(339,\cdot)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{484}(355,\cdot)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{484}(367,\cdot)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{484}(379,\cdot)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$