Dirichlet character χ297(284,⋅)\chi_{297}(284,\cdot)

• Label: 297.284
• Modulus: $297$
• Conductor: $297$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$297$
Conductor:	$297$
Order:	$90$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 297.v

$\chi_{297}(5,\cdot)$ $\chi_{297}(14,\cdot)$ $\chi_{297}(20,\cdot)$ $\chi_{297}(38,\cdot)$ $\chi_{297}(47,\cdot)$ $\chi_{297}(59,\cdot)$ $\chi_{297}(86,\cdot)$ $\chi_{297}(92,\cdot)$ $\chi_{297}(104,\cdot)$ $\chi_{297}(113,\cdot)$ $\chi_{297}(119,\cdot)$ $\chi_{297}(137,\cdot)$ $\chi_{297}(146,\cdot)$ $\chi_{297}(158,\cdot)$ $\chi_{297}(185,\cdot)$ $\chi_{297}(191,\cdot)$ $\chi_{297}(203,\cdot)$ $\chi_{297}(212,\cdot)$ $\chi_{297}(218,\cdot)$ $\chi_{297}(236,\cdot)$ $\chi_{297}(245,\cdot)$ $\chi_{297}(257,\cdot)$ $\chi_{297}(284,\cdot)$ $\chi_{297}(290,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

$(56,244)$ → $(e\left(\frac{17}{18}\right),e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 297 }(284, a)$	$-1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{30}\right)$

Gauss sum

Jacobi sum

Kloosterman sum