Dirichlet character χ1859(9,⋅)\chi_{1859}(9,\cdot)

• Label: 1859.9
• Modulus: $1859$
• Conductor: $1859$
• Order: $195$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1859$
Conductor:	$1859$
Order:	$195$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1859.bo

$\chi_{1859}(3,\cdot)$ $\chi_{1859}(9,\cdot)$ $\chi_{1859}(16,\cdot)$ $\chi_{1859}(42,\cdot)$ $\chi_{1859}(48,\cdot)$ $\chi_{1859}(81,\cdot)$ $\chi_{1859}(113,\cdot)$ $\chi_{1859}(126,\cdot)$ $\chi_{1859}(152,\cdot)$ $\chi_{1859}(159,\cdot)$ $\chi_{1859}(185,\cdot)$ $\chi_{1859}(224,\cdot)$ $\chi_{1859}(256,\cdot)$ $\chi_{1859}(269,\cdot)$ $\chi_{1859}(289,\cdot)$ $\chi_{1859}(295,\cdot)$ $\chi_{1859}(302,\cdot)$ $\chi_{1859}(328,\cdot)$ $\chi_{1859}(334,\cdot)$ $\chi_{1859}(367,\cdot)$ $\chi_{1859}(399,\cdot)$ $\chi_{1859}(412,\cdot)$ $\chi_{1859}(432,\cdot)$ $\chi_{1859}(438,\cdot)$ $\chi_{1859}(445,\cdot)$ $\chi_{1859}(471,\cdot)$ $\chi_{1859}(477,\cdot)$ $\chi_{1859}(510,\cdot)$ $\chi_{1859}(542,\cdot)$ $\chi_{1859}(555,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{195})$
Fixed field:	Number field defined by a degree 195 polynomial (not computed)

Values on generators

$(508,1354)$ → $(e\left(\frac{3}{5}\right),e\left(\frac{23}{39}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 1859 }(9, a)$	$1$	$1$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{13}\right)$