Dirichlet character \(\chi_{2032}(83,\cdot)\)

• Label: 2032.83
• Modulus: $2032$
• Conductor: $2032$
• Order: $252$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2032\)
Conductor:	\(2032\)
Order:	\(252\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2032.cq

\(\chi_{2032}(3,\cdot)\) \(\chi_{2032}(43,\cdot)\) \(\chi_{2032}(67,\cdot)\) \(\chi_{2032}(83,\cdot)\) \(\chi_{2032}(91,\cdot)\) \(\chi_{2032}(139,\cdot)\) \(\chi_{2032}(219,\cdot)\) \(\chi_{2032}(243,\cdot)\) \(\chi_{2032}(283,\cdot)\) \(\chi_{2032}(299,\cdot)\) \(\chi_{2032}(307,\cdot)\) \(\chi_{2032}(339,\cdot)\) \(\chi_{2032}(347,\cdot)\) \(\chi_{2032}(355,\cdot)\) \(\chi_{2032}(363,\cdot)\) \(\chi_{2032}(387,\cdot)\) \(\chi_{2032}(395,\cdot)\) \(\chi_{2032}(427,\cdot)\) \(\chi_{2032}(459,\cdot)\) \(\chi_{2032}(467,\cdot)\) \(\chi_{2032}(491,\cdot)\) \(\chi_{2032}(499,\cdot)\) \(\chi_{2032}(515,\cdot)\) \(\chi_{2032}(531,\cdot)\) \(\chi_{2032}(547,\cdot)\) \(\chi_{2032}(563,\cdot)\) \(\chi_{2032}(683,\cdot)\) \(\chi_{2032}(691,\cdot)\) \(\chi_{2032}(731,\cdot)\) \(\chi_{2032}(747,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{252})$
Fixed field:	Number field defined by a degree 252 polynomial (not computed)

Values on generators

\((255,1525,257)\) → \((-1,-i,e\left(\frac{23}{126}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 2032 }(83, a) \)	\(1\)	\(1\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{167}{252}\right)\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{233}{252}\right)\)