Dirichlet character \(\chi_{1573}(1005,\cdot)\)

• Label: 1573.1005
• Modulus: $1573$
• Conductor: $1573$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1573\)
Conductor:	\(1573\)
Order:	\(330\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1573.bs

\(\chi_{1573}(4,\cdot)\) \(\chi_{1573}(36,\cdot)\) \(\chi_{1573}(49,\cdot)\) \(\chi_{1573}(69,\cdot)\) \(\chi_{1573}(75,\cdot)\) \(\chi_{1573}(82,\cdot)\) \(\chi_{1573}(108,\cdot)\) \(\chi_{1573}(114,\cdot)\) \(\chi_{1573}(147,\cdot)\) \(\chi_{1573}(179,\cdot)\) \(\chi_{1573}(192,\cdot)\) \(\chi_{1573}(212,\cdot)\) \(\chi_{1573}(218,\cdot)\) \(\chi_{1573}(225,\cdot)\) \(\chi_{1573}(257,\cdot)\) \(\chi_{1573}(290,\cdot)\) \(\chi_{1573}(322,\cdot)\) \(\chi_{1573}(335,\cdot)\) \(\chi_{1573}(355,\cdot)\) \(\chi_{1573}(361,\cdot)\) \(\chi_{1573}(368,\cdot)\) \(\chi_{1573}(394,\cdot)\) \(\chi_{1573}(400,\cdot)\) \(\chi_{1573}(433,\cdot)\) \(\chi_{1573}(465,\cdot)\) \(\chi_{1573}(478,\cdot)\) \(\chi_{1573}(498,\cdot)\) \(\chi_{1573}(504,\cdot)\) \(\chi_{1573}(537,\cdot)\) \(\chi_{1573}(543,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

\((365,1211)\) → \((e\left(\frac{21}{55}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 1573 }(1005, a) \)	\(1\)	\(1\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)