Dirichlet character \(\chi_{297}(137,\cdot)\)

• Label: 297.137
• 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

\((56,244)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{2}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 297 }(137, a) \)	\(-1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum