Dirichlet character \(\chi_{2303}(222,\cdot)\)

• Label: 2303.222
• Modulus: $2303$
• Conductor: $2303$
• Order: $966$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2303\)
Conductor:	\(2303\)
Order:	\(966\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2303.bf

\(\chi_{2303}(3,\cdot)\) \(\chi_{2303}(12,\cdot)\) \(\chi_{2303}(17,\cdot)\) \(\chi_{2303}(24,\cdot)\) \(\chi_{2303}(54,\cdot)\) \(\chi_{2303}(59,\cdot)\) \(\chi_{2303}(61,\cdot)\) \(\chi_{2303}(75,\cdot)\) \(\chi_{2303}(89,\cdot)\) \(\chi_{2303}(96,\cdot)\) \(\chi_{2303}(101,\cdot)\) \(\chi_{2303}(103,\cdot)\) \(\chi_{2303}(108,\cdot)\) \(\chi_{2303}(110,\cdot)\) \(\chi_{2303}(115,\cdot)\) \(\chi_{2303}(122,\cdot)\) \(\chi_{2303}(131,\cdot)\) \(\chi_{2303}(136,\cdot)\) \(\chi_{2303}(143,\cdot)\) \(\chi_{2303}(145,\cdot)\) \(\chi_{2303}(150,\cdot)\) \(\chi_{2303}(157,\cdot)\) \(\chi_{2303}(159,\cdot)\) \(\chi_{2303}(173,\cdot)\) \(\chi_{2303}(192,\cdot)\) \(\chi_{2303}(194,\cdot)\) \(\chi_{2303}(206,\cdot)\) \(\chi_{2303}(213,\cdot)\) \(\chi_{2303}(220,\cdot)\) \(\chi_{2303}(222,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{483})$
Fixed field:	Number field defined by a degree 966 polynomial (not computed)

Values on generators

\((2257,99)\) → \((e\left(\frac{17}{42}\right),e\left(\frac{17}{23}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 2303 }(222, a) \)	\(-1\)	\(1\)	\(e\left(\frac{400}{483}\right)\)	\(e\left(\frac{181}{966}\right)\)	\(e\left(\frac{317}{483}\right)\)	\(e\left(\frac{461}{966}\right)\)	\(e\left(\frac{5}{322}\right)\)	\(e\left(\frac{78}{161}\right)\)	\(e\left(\frac{181}{483}\right)\)	\(e\left(\frac{295}{966}\right)\)	\(e\left(\frac{176}{483}\right)\)	\(e\left(\frac{815}{966}\right)\)