Dirichlet character χ297(7,⋅)\chi_{297}(7,\cdot)

• Label: 297.7
• 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.w

$\chi_{297}(7,\cdot)$ $\chi_{297}(13,\cdot)$ $\chi_{297}(40,\cdot)$ $\chi_{297}(52,\cdot)$ $\chi_{297}(61,\cdot)$ $\chi_{297}(79,\cdot)$ $\chi_{297}(85,\cdot)$ $\chi_{297}(94,\cdot)$ $\chi_{297}(106,\cdot)$ $\chi_{297}(112,\cdot)$ $\chi_{297}(139,\cdot)$ $\chi_{297}(151,\cdot)$ $\chi_{297}(160,\cdot)$ $\chi_{297}(178,\cdot)$ $\chi_{297}(184,\cdot)$ $\chi_{297}(193,\cdot)$ $\chi_{297}(205,\cdot)$ $\chi_{297}(211,\cdot)$ $\chi_{297}(238,\cdot)$ $\chi_{297}(250,\cdot)$ $\chi_{297}(259,\cdot)$ $\chi_{297}(277,\cdot)$ $\chi_{297}(283,\cdot)$ $\chi_{297}(292,\cdot)$

Related number fields

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

Values on generators

$(56,244)$ → $(e\left(\frac{8}{9}\right),e\left(\frac{7}{10}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 297 }(7, a)$	$-1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{30}\right)$

Gauss sum

Jacobi sum

Kloosterman sum