Dirichlet character χ4205(418,⋅)\chi_{4205}(418,\cdot)

• Label: 4205.418
• 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.y

$\chi_{4205}(17,\cdot)$ $\chi_{4205}(128,\cdot)$ $\chi_{4205}(162,\cdot)$ $\chi_{4205}(273,\cdot)$ $\chi_{4205}(307,\cdot)$ $\chi_{4205}(418,\cdot)$ $\chi_{4205}(452,\cdot)$ $\chi_{4205}(563,\cdot)$ $\chi_{4205}(597,\cdot)$ $\chi_{4205}(708,\cdot)$ $\chi_{4205}(742,\cdot)$ $\chi_{4205}(853,\cdot)$ $\chi_{4205}(887,\cdot)$ $\chi_{4205}(998,\cdot)$ $\chi_{4205}(1032,\cdot)$ $\chi_{4205}(1143,\cdot)$ $\chi_{4205}(1177,\cdot)$ $\chi_{4205}(1288,\cdot)$ $\chi_{4205}(1322,\cdot)$ $\chi_{4205}(1433,\cdot)$ $\chi_{4205}(1467,\cdot)$ $\chi_{4205}(1578,\cdot)$ $\chi_{4205}(1612,\cdot)$ $\chi_{4205}(1757,\cdot)$ $\chi_{4205}(1868,\cdot)$ $\chi_{4205}(1902,\cdot)$ $\chi_{4205}(2013,\cdot)$ $\chi_{4205}(2047,\cdot)$ $\chi_{4205}(2158,\cdot)$ $\chi_{4205}(2192,\cdot)$ ...

Related number fields

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

Values on generators

$(842,3366)$ → $(-i,e\left(\frac{101}{116}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 4205 }(418, a)$	$1$	$1$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{75}{116}\right)$