Dirichlet character \(\chi_{2864}(115,\cdot)\)

• Label: 2864.115
• Modulus: $2864$
• Conductor: $2864$
• Order: $356$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2864\)
Conductor:	\(2864\)
Order:	\(356\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2864.x

\(\chi_{2864}(11,\cdot)\) \(\chi_{2864}(35,\cdot)\) \(\chi_{2864}(91,\cdot)\) \(\chi_{2864}(99,\cdot)\) \(\chi_{2864}(115,\cdot)\) \(\chi_{2864}(123,\cdot)\) \(\chi_{2864}(131,\cdot)\) \(\chi_{2864}(163,\cdot)\) \(\chi_{2864}(187,\cdot)\) \(\chi_{2864}(203,\cdot)\) \(\chi_{2864}(211,\cdot)\) \(\chi_{2864}(219,\cdot)\) \(\chi_{2864}(251,\cdot)\) \(\chi_{2864}(275,\cdot)\) \(\chi_{2864}(283,\cdot)\) \(\chi_{2864}(291,\cdot)\) \(\chi_{2864}(299,\cdot)\) \(\chi_{2864}(307,\cdot)\) \(\chi_{2864}(315,\cdot)\) \(\chi_{2864}(331,\cdot)\) \(\chi_{2864}(339,\cdot)\) \(\chi_{2864}(355,\cdot)\) \(\chi_{2864}(379,\cdot)\) \(\chi_{2864}(395,\cdot)\) \(\chi_{2864}(411,\cdot)\) \(\chi_{2864}(427,\cdot)\) \(\chi_{2864}(467,\cdot)\) \(\chi_{2864}(491,\cdot)\) \(\chi_{2864}(515,\cdot)\) \(\chi_{2864}(523,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{356})$
Fixed field:	Number field defined by a degree 356 polynomial (not computed)

Values on generators

\((1791,2149,897)\) → \((-1,-i,e\left(\frac{95}{178}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 2864 }(115, a) \)	\(1\)	\(1\)	\(e\left(\frac{139}{356}\right)\)	\(e\left(\frac{143}{356}\right)\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{139}{178}\right)\)	\(e\left(\frac{91}{356}\right)\)	\(e\left(\frac{33}{356}\right)\)	\(e\left(\frac{141}{178}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{203}{356}\right)\)	\(e\left(\frac{233}{356}\right)\)