Dirichlet character orbit 4675.jh

• Label: 4675.jh
• Modulus: $4675$
• Conductor: $4675$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4675$
Conductor:	$4675$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{4675}(48,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{80}\right)$	$i$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{4675}(317,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{63}{80}\right)$	$-i$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{4675}(388,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{49}{80}\right)$	$i$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{4675}(487,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{79}{80}\right)$	$-i$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{4675}(598,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{80}\right)$	$i$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{4675}(658,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{53}{80}\right)$	$i$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{4675}(753,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{77}{80}\right)$	$i$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{4675}(938,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{80}\right)$	$i$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{4675}(1027,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{51}{80}\right)$	$-i$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{4675}(1302,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{80}\right)$	$-i$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{4675}(1417,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{80}\right)$	$-i$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{4675}(1423,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{80}\right)$	$i$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{4675}(1578,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{80}\right)$	$i$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{4675}(1587,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{39}{80}\right)$	$-i$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{4675}(1622,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{67}{80}\right)$	$-i$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{4675}(1763,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{69}{80}\right)$	$i$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{4675}(1897,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{80}\right)$	$-i$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{4675}(2128,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{57}{80}\right)$	$i$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{4675}(2952,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{80}\right)$	$-i$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{4675}(2953,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{80}\right)$	$i$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{4675}(3067,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{80}\right)$	$-i$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{4675}(3133,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{80}\right)$	$i$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{4675}(3237,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{80}\right)$	$-i$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{4675}(3342,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{80}\right)$	$-i$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{4675}(3512,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{59}{80}\right)$	$-i$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{4675}(3547,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{47}{80}\right)$	$-i$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{4675}(3898,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{61}{80}\right)$	$i$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{4675}(3958,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{33}{80}\right)$	$i$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{4675}(4052,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{71}{80}\right)$	$-i$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{4675}(4238,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{80}\right)$	$i$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{4675}(4508,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{73}{80}\right)$	$i$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{80}\right)$