Dirichlet character χ1617(1007,⋅)\chi_{1617}(1007,\cdot)

• Label: 1617.1007
• Modulus: $1617$
• Conductor: $1617$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1617$
Conductor:	$1617$
Order:	$70$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1617.cd

$\chi_{1617}(41,\cdot)$ $\chi_{1617}(62,\cdot)$ $\chi_{1617}(83,\cdot)$ $\chi_{1617}(167,\cdot)$ $\chi_{1617}(272,\cdot)$ $\chi_{1617}(314,\cdot)$ $\chi_{1617}(398,\cdot)$ $\chi_{1617}(503,\cdot)$ $\chi_{1617}(524,\cdot)$ $\chi_{1617}(545,\cdot)$ $\chi_{1617}(629,\cdot)$ $\chi_{1617}(755,\cdot)$ $\chi_{1617}(776,\cdot)$ $\chi_{1617}(860,\cdot)$ $\chi_{1617}(965,\cdot)$ $\chi_{1617}(986,\cdot)$ $\chi_{1617}(1007,\cdot)$ $\chi_{1617}(1091,\cdot)$ $\chi_{1617}(1196,\cdot)$ $\chi_{1617}(1217,\cdot)$ $\chi_{1617}(1238,\cdot)$ $\chi_{1617}(1427,\cdot)$ $\chi_{1617}(1448,\cdot)$ $\chi_{1617}(1553,\cdot)$

Related number fields

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

Values on generators

$(1079,199,442)$ → $(-1,e\left(\frac{1}{14}\right),e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{ 1617 }(1007, a)$	$-1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{35}\right)$