Dirichlet character orbit 4675.ih

• Label: 4675.ih
• 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{4675}(58,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{4675}(267,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{4675}(313,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{4675}(333,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{4675}(422,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{4675}(588,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{4675}(653,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{4675}(702,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{4675}(823,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{4675}(928,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{4675}(972,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{4675}(1098,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{4675}(1527,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{4675}(1797,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{4675}(1983,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{4675}(2062,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{4675}(2077,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{4675}(2238,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{4675}(2578,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{4675}(2742,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{4675}(2748,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{4675}(2887,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{4675}(2902,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{4675}(3083,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{4675}(3338,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{4675}(3437,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{4675}(3567,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{4675}(3678,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{4675}(3848,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{4675}(4117,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{4675}(4262,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{80}\right)$