Dirichlet character \(\chi_{31360}(37,\cdot)\)

• Label: 31360.37
• Modulus: $31360$
• Conductor: $31360$
• Order: $672$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(31360\)
Conductor:	\(31360\)
Order:	\(672\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 31360.na

\(\chi_{31360}(37,\cdot)\) \(\chi_{31360}(93,\cdot)\) \(\chi_{31360}(277,\cdot)\) \(\chi_{31360}(333,\cdot)\) \(\chi_{31360}(597,\cdot)\) \(\chi_{31360}(653,\cdot)\) \(\chi_{31360}(837,\cdot)\) \(\chi_{31360}(893,\cdot)\) \(\chi_{31360}(1213,\cdot)\) \(\chi_{31360}(1397,\cdot)\) \(\chi_{31360}(1453,\cdot)\) \(\chi_{31360}(1717,\cdot)\) \(\chi_{31360}(1773,\cdot)\) \(\chi_{31360}(1957,\cdot)\) \(\chi_{31360}(2013,\cdot)\) \(\chi_{31360}(2277,\cdot)\) \(\chi_{31360}(2573,\cdot)\) \(\chi_{31360}(2837,\cdot)\) \(\chi_{31360}(2893,\cdot)\) \(\chi_{31360}(3077,\cdot)\) \(\chi_{31360}(3133,\cdot)\) \(\chi_{31360}(3397,\cdot)\) \(\chi_{31360}(3453,\cdot)\) \(\chi_{31360}(3637,\cdot)\) \(\chi_{31360}(3957,\cdot)\) \(\chi_{31360}(4013,\cdot)\) \(\chi_{31360}(4197,\cdot)\) \(\chi_{31360}(4253,\cdot)\) \(\chi_{31360}(4517,\cdot)\) \(\chi_{31360}(4573,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{672})$
Fixed field:	Number field defined by a degree 672 polynomial (not computed)

Values on generators

\((17151,28421,18817,10881)\) → \((1,e\left(\frac{25}{32}\right),i,e\left(\frac{16}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 31360 }(37, a) \)	\(-1\)	\(1\)	\(e\left(\frac{575}{672}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{593}{672}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{127}{224}\right)\)	\(e\left(\frac{69}{224}\right)\)	\(e\left(\frac{7}{12}\right)\)