Dirichlet character χ4205(1897,⋅)\chi_{4205}(1897,\cdot)

• Label: 4205.1897
• Modulus: $4205$
• Conductor: $4205$
• Order: $116$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4205$
Conductor:	$4205$
Order:	$116$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4205.bd

$\chi_{4205}(12,\cdot)$ $\chi_{4205}(133,\cdot)$ $\chi_{4205}(157,\cdot)$ $\chi_{4205}(278,\cdot)$ $\chi_{4205}(302,\cdot)$ $\chi_{4205}(423,\cdot)$ $\chi_{4205}(447,\cdot)$ $\chi_{4205}(568,\cdot)$ $\chi_{4205}(592,\cdot)$ $\chi_{4205}(713,\cdot)$ $\chi_{4205}(737,\cdot)$ $\chi_{4205}(858,\cdot)$ $\chi_{4205}(1003,\cdot)$ $\chi_{4205}(1027,\cdot)$ $\chi_{4205}(1148,\cdot)$ $\chi_{4205}(1172,\cdot)$ $\chi_{4205}(1293,\cdot)$ $\chi_{4205}(1317,\cdot)$ $\chi_{4205}(1438,\cdot)$ $\chi_{4205}(1462,\cdot)$ $\chi_{4205}(1583,\cdot)$ $\chi_{4205}(1607,\cdot)$ $\chi_{4205}(1728,\cdot)$ $\chi_{4205}(1752,\cdot)$ $\chi_{4205}(1873,\cdot)$ $\chi_{4205}(1897,\cdot)$ $\chi_{4205}(2018,\cdot)$ $\chi_{4205}(2042,\cdot)$ $\chi_{4205}(2163,\cdot)$ $\chi_{4205}(2187,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{116})$
Fixed field:	Number field defined by a degree 116 polynomial (not computed)

Values on generators

$(842,3366)$ → $(i,e\left(\frac{89}{116}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 4205 }(1897, a)$	$1$	$1$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{77}{116}\right)$