Dirichlet character \(\chi_{31360}(7853,\cdot)\)

• Label: 31360.7853
• Modulus: $31360$
• Conductor: $31360$
• Order: $224$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(31360\)
Conductor:	\(31360\)
Order:	\(224\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 31360.lv

\(\chi_{31360}(13,\cdot)\) \(\chi_{31360}(517,\cdot)\) \(\chi_{31360}(573,\cdot)\) \(\chi_{31360}(1133,\cdot)\) \(\chi_{31360}(1637,\cdot)\) \(\chi_{31360}(1693,\cdot)\) \(\chi_{31360}(2197,\cdot)\) \(\chi_{31360}(2757,\cdot)\) \(\chi_{31360}(2813,\cdot)\) \(\chi_{31360}(3317,\cdot)\) \(\chi_{31360}(3373,\cdot)\) \(\chi_{31360}(3877,\cdot)\) \(\chi_{31360}(3933,\cdot)\) \(\chi_{31360}(4437,\cdot)\) \(\chi_{31360}(4493,\cdot)\) \(\chi_{31360}(5053,\cdot)\) \(\chi_{31360}(5557,\cdot)\) \(\chi_{31360}(5613,\cdot)\) \(\chi_{31360}(6117,\cdot)\) \(\chi_{31360}(6677,\cdot)\) \(\chi_{31360}(6733,\cdot)\) \(\chi_{31360}(7237,\cdot)\) \(\chi_{31360}(7293,\cdot)\) \(\chi_{31360}(7797,\cdot)\) \(\chi_{31360}(7853,\cdot)\) \(\chi_{31360}(8357,\cdot)\) \(\chi_{31360}(8413,\cdot)\) \(\chi_{31360}(8973,\cdot)\) \(\chi_{31360}(9477,\cdot)\) \(\chi_{31360}(9533,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{224})$
Fixed field:	Number field defined by a degree 224 polynomial (not computed)

Values on generators

\((17151,28421,18817,10881)\) → \((1,e\left(\frac{7}{32}\right),-i,e\left(\frac{11}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 31360 }(7853, a) \)	\(1\)	\(1\)	\(e\left(\frac{155}{224}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{17}{224}\right)\)	\(e\left(\frac{123}{224}\right)\)	\(i\)