Dirichlet character \(\chi_{4563}(1312,\cdot)\)

• Label: 4563.1312
• Modulus: $4563$
• Conductor: $4563$
• Order: $234$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4563\)
Conductor:	\(4563\)
Order:	\(234\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4563.dh

\(\chi_{4563}(25,\cdot)\) \(\chi_{4563}(103,\cdot)\) \(\chi_{4563}(142,\cdot)\) \(\chi_{4563}(220,\cdot)\) \(\chi_{4563}(259,\cdot)\) \(\chi_{4563}(376,\cdot)\) \(\chi_{4563}(454,\cdot)\) \(\chi_{4563}(493,\cdot)\) \(\chi_{4563}(571,\cdot)\) \(\chi_{4563}(610,\cdot)\) \(\chi_{4563}(688,\cdot)\) \(\chi_{4563}(727,\cdot)\) \(\chi_{4563}(805,\cdot)\) \(\chi_{4563}(922,\cdot)\) \(\chi_{4563}(961,\cdot)\) \(\chi_{4563}(1039,\cdot)\) \(\chi_{4563}(1078,\cdot)\) \(\chi_{4563}(1156,\cdot)\) \(\chi_{4563}(1195,\cdot)\) \(\chi_{4563}(1273,\cdot)\) \(\chi_{4563}(1312,\cdot)\) \(\chi_{4563}(1390,\cdot)\) \(\chi_{4563}(1429,\cdot)\) \(\chi_{4563}(1507,\cdot)\) \(\chi_{4563}(1546,\cdot)\) \(\chi_{4563}(1624,\cdot)\) \(\chi_{4563}(1663,\cdot)\) \(\chi_{4563}(1741,\cdot)\) \(\chi_{4563}(1780,\cdot)\) \(\chi_{4563}(1897,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{117})$
Fixed field:	Number field defined by a degree 234 polynomial (not computed)

Values on generators

\((677,3889)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{15}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(1312, a) \)	\(1\)	\(1\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{67}{234}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{23}{117}\right)\)	\(e\left(\frac{22}{39}\right)\)