Dirichlet character orbit 725.bh

• Label: 725.bh
• Modulus: $725$
• Conductor: $725$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$725$
Conductor:	$725$
Order:	$70$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{725}(4,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{70}\right)$
$\chi_{725}(9,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{725}(34,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{725}(64,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{725}(109,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{70}\right)$
$\chi_{725}(129,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{70}\right)$
$\chi_{725}(154,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{70}\right)$
$\chi_{725}(179,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{70}\right)$
$\chi_{725}(209,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{70}\right)$
$\chi_{725}(254,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{725}(294,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{725}(354,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{725}(419,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{725}(439,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{725}(444,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{725}(469,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{70}\right)$
$\chi_{725}(544,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{725}(564,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{725}(584,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{725}(589,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{70}\right)$
$\chi_{725}(614,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{725}(644,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{725}(689,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{70}\right)$
$\chi_{725}(709,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{61}{70}\right)$