Dirichlet character χ725(34,⋅)\chi_{725}(34,\cdot)

• Label: 725.34
• 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

Galois orbit 725.bh

$\chi_{725}(4,\cdot)$ $\chi_{725}(9,\cdot)$ $\chi_{725}(34,\cdot)$ $\chi_{725}(64,\cdot)$ $\chi_{725}(109,\cdot)$ $\chi_{725}(129,\cdot)$ $\chi_{725}(154,\cdot)$ $\chi_{725}(179,\cdot)$ $\chi_{725}(209,\cdot)$ $\chi_{725}(254,\cdot)$ $\chi_{725}(294,\cdot)$ $\chi_{725}(354,\cdot)$ $\chi_{725}(419,\cdot)$ $\chi_{725}(439,\cdot)$ $\chi_{725}(444,\cdot)$ $\chi_{725}(469,\cdot)$ $\chi_{725}(544,\cdot)$ $\chi_{725}(564,\cdot)$ $\chi_{725}(584,\cdot)$ $\chi_{725}(589,\cdot)$ $\chi_{725}(614,\cdot)$ $\chi_{725}(644,\cdot)$ $\chi_{725}(689,\cdot)$ $\chi_{725}(709,\cdot)$

Related number fields

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

Values on generators

$(552,176)$ → $(e\left(\frac{7}{10}\right),e\left(\frac{11}{14}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 725 }(34, a)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{70}\right)$

Gauss sum

Jacobi sum

Kloosterman sum