Dirichlet character orbit 107.c

• Label: 107.c
• Modulus: $107$
• Conductor: $107$
• Order: $53$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$107$
Conductor:	$107$
Order:	$53$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{53})$
Fixed field:	Number field defined by a degree 53 polynomial

First 31 of 52 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{107}(3,\cdot)$	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{28}{53}\right)$
$\chi_{107}(4,\cdot)$	$1$	$1$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{22}{53}\right)$
$\chi_{107}(9,\cdot)$	$1$	$1$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{3}{53}\right)$
$\chi_{107}(10,\cdot)$	$1$	$1$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{51}{53}\right)$
$\chi_{107}(11,\cdot)$	$1$	$1$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{30}{53}\right)$
$\chi_{107}(12,\cdot)$	$1$	$1$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{50}{53}\right)$
$\chi_{107}(13,\cdot)$	$1$	$1$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{48}{53}\right)$
$\chi_{107}(14,\cdot)$	$1$	$1$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{7}{53}\right)$
$\chi_{107}(16,\cdot)$	$1$	$1$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{44}{53}\right)$
$\chi_{107}(19,\cdot)$	$1$	$1$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{10}{53}\right)$
$\chi_{107}(23,\cdot)$	$1$	$1$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{46}{53}\right)$
$\chi_{107}(25,\cdot)$	$1$	$1$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{27}{53}\right)$
$\chi_{107}(27,\cdot)$	$1$	$1$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{31}{53}\right)$
$\chi_{107}(29,\cdot)$	$1$	$1$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{34}{53}\right)$
$\chi_{107}(30,\cdot)$	$1$	$1$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{26}{53}\right)$
$\chi_{107}(33,\cdot)$	$1$	$1$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{5}{53}\right)$
$\chi_{107}(34,\cdot)$	$1$	$1$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{12}{53}\right)$
$\chi_{107}(35,\cdot)$	$1$	$1$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{36}{53}\right)$
$\chi_{107}(36,\cdot)$	$1$	$1$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{25}{53}\right)$
$\chi_{107}(37,\cdot)$	$1$	$1$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{47}{53}\right)$
$\chi_{107}(39,\cdot)$	$1$	$1$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{23}{53}\right)$
$\chi_{107}(40,\cdot)$	$1$	$1$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{20}{53}\right)$
$\chi_{107}(41,\cdot)$	$1$	$1$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{16}{53}\right)$
$\chi_{107}(42,\cdot)$	$1$	$1$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{35}{53}\right)$
$\chi_{107}(44,\cdot)$	$1$	$1$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{52}{53}\right)$
$\chi_{107}(47,\cdot)$	$1$	$1$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{37}{53}\right)$
$\chi_{107}(48,\cdot)$	$1$	$1$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{19}{53}\right)$
$\chi_{107}(49,\cdot)$	$1$	$1$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{45}{53}\right)$
$\chi_{107}(52,\cdot)$	$1$	$1$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{17}{53}\right)$
$\chi_{107}(53,\cdot)$	$1$	$1$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{42}{53}\right)$
$\chi_{107}(56,\cdot)$	$1$	$1$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{29}{53}\right)$