Dirichlet character orbit 3267.ba

• Label: 3267.ba
• Modulus: $3267$
• Conductor: $121$
• Order: $55$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3267$
Conductor:	$121$
Order:	$55$
Real:	no
Primitive:	no, induced from 121.g
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 55 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{3267}(82,\cdot)$	$1$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{3267}(136,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{3267}(163,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{3267}(190,\cdot)$	$1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{3267}(379,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{3267}(433,\cdot)$	$1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{3267}(460,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{3267}(676,\cdot)$	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{3267}(730,\cdot)$	$1$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{3267}(757,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{3267}(784,\cdot)$	$1$	$1$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{3267}(973,\cdot)$	$1$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{3267}(1027,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{3267}(1054,\cdot)$	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{3267}(1081,\cdot)$	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{3267}(1270,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{3267}(1324,\cdot)$	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{3267}(1351,\cdot)$	$1$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{3267}(1378,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{3267}(1567,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{3267}(1621,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{3267}(1648,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{3267}(1675,\cdot)$	$1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{3267}(1864,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{3267}(1918,\cdot)$	$1$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{3267}(1972,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{3267}(2161,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{3267}(2215,\cdot)$	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{3267}(2242,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{3267}(2269,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{3267}(2458,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{23}{55}\right)$