Dirichlet character \(\chi_{2032}(13,\cdot)\)

• Label: 2032.13
• 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.ct

\(\chi_{2032}(13,\cdot)\) \(\chi_{2032}(21,\cdot)\) \(\chi_{2032}(69,\cdot)\) \(\chi_{2032}(157,\cdot)\) \(\chi_{2032}(189,\cdot)\) \(\chi_{2032}(197,\cdot)\) \(\chi_{2032}(269,\cdot)\) \(\chi_{2032}(285,\cdot)\) \(\chi_{2032}(325,\cdot)\) \(\chi_{2032}(333,\cdot)\) \(\chi_{2032}(453,\cdot)\) \(\chi_{2032}(469,\cdot)\) \(\chi_{2032}(485,\cdot)\) \(\chi_{2032}(501,\cdot)\) \(\chi_{2032}(517,\cdot)\) \(\chi_{2032}(525,\cdot)\) \(\chi_{2032}(549,\cdot)\) \(\chi_{2032}(557,\cdot)\) \(\chi_{2032}(589,\cdot)\) \(\chi_{2032}(621,\cdot)\) \(\chi_{2032}(629,\cdot)\) \(\chi_{2032}(653,\cdot)\) \(\chi_{2032}(661,\cdot)\) \(\chi_{2032}(669,\cdot)\) \(\chi_{2032}(677,\cdot)\) \(\chi_{2032}(709,\cdot)\) \(\chi_{2032}(717,\cdot)\) \(\chi_{2032}(733,\cdot)\) \(\chi_{2032}(773,\cdot)\) \(\chi_{2032}(797,\cdot)\) ...

Related number fields

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

Values on generators

\((255,1525,257)\) → \((1,-i,e\left(\frac{47}{63}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 2032 }(13, a) \)	\(1\)	\(1\)	\(e\left(\frac{251}{252}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{252}\right)\)