Dirichlet character \(\chi_{1712}(461,\cdot)\)

• Label: 1712.461
• Modulus: $1712$
• Conductor: $1712$
• Order: $212$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1712\)
Conductor:	\(1712\)
Order:	\(212\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1712.w

\(\chi_{1712}(13,\cdot)\) \(\chi_{1712}(29,\cdot)\) \(\chi_{1712}(37,\cdot)\) \(\chi_{1712}(53,\cdot)\) \(\chi_{1712}(61,\cdot)\) \(\chi_{1712}(69,\cdot)\) \(\chi_{1712}(85,\cdot)\) \(\chi_{1712}(101,\cdot)\) \(\chi_{1712}(117,\cdot)\) \(\chi_{1712}(141,\cdot)\) \(\chi_{1712}(149,\cdot)\) \(\chi_{1712}(197,\cdot)\) \(\chi_{1712}(237,\cdot)\) \(\chi_{1712}(253,\cdot)\) \(\chi_{1712}(261,\cdot)\) \(\chi_{1712}(293,\cdot)\) \(\chi_{1712}(301,\cdot)\) \(\chi_{1712}(325,\cdot)\) \(\chi_{1712}(333,\cdot)\) \(\chi_{1712}(357,\cdot)\) \(\chi_{1712}(365,\cdot)\) \(\chi_{1712}(373,\cdot)\) \(\chi_{1712}(397,\cdot)\) \(\chi_{1712}(413,\cdot)\) \(\chi_{1712}(421,\cdot)\) \(\chi_{1712}(437,\cdot)\) \(\chi_{1712}(453,\cdot)\) \(\chi_{1712}(461,\cdot)\) \(\chi_{1712}(469,\cdot)\) \(\chi_{1712}(477,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{212})$
Fixed field:	Number field defined by a degree 212 polynomial (not computed)

Values on generators

\((1071,1285,1393)\) → \((1,-i,e\left(\frac{46}{53}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1712 }(461, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{212}\right)\)	\(e\left(\frac{115}{212}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{179}{212}\right)\)	\(e\left(\frac{85}{212}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{201}{212}\right)\)	\(e\left(\frac{175}{212}\right)\)