Dirichlet character \(\chi_{4563}(1453,\cdot)\)

• Label: 4563.1453
• 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.de

\(\chi_{4563}(43,\cdot)\) \(\chi_{4563}(49,\cdot)\) \(\chi_{4563}(160,\cdot)\) \(\chi_{4563}(166,\cdot)\) \(\chi_{4563}(277,\cdot)\) \(\chi_{4563}(283,\cdot)\) \(\chi_{4563}(394,\cdot)\) \(\chi_{4563}(400,\cdot)\) \(\chi_{4563}(511,\cdot)\) \(\chi_{4563}(517,\cdot)\) \(\chi_{4563}(628,\cdot)\) \(\chi_{4563}(634,\cdot)\) \(\chi_{4563}(745,\cdot)\) \(\chi_{4563}(751,\cdot)\) \(\chi_{4563}(862,\cdot)\) \(\chi_{4563}(979,\cdot)\) \(\chi_{4563}(985,\cdot)\) \(\chi_{4563}(1096,\cdot)\) \(\chi_{4563}(1102,\cdot)\) \(\chi_{4563}(1213,\cdot)\) \(\chi_{4563}(1219,\cdot)\) \(\chi_{4563}(1336,\cdot)\) \(\chi_{4563}(1447,\cdot)\) \(\chi_{4563}(1453,\cdot)\) \(\chi_{4563}(1564,\cdot)\) \(\chi_{4563}(1570,\cdot)\) \(\chi_{4563}(1681,\cdot)\) \(\chi_{4563}(1687,\cdot)\) \(\chi_{4563}(1798,\cdot)\) \(\chi_{4563}(1804,\cdot)\) ...

Related number fields

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

Values on generators

\((677,3889)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{35}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 4563 }(1453, a) \)	\(1\)	\(1\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{53}{117}\right)\)	\(e\left(\frac{217}{234}\right)\)	\(e\left(\frac{107}{234}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{106}{117}\right)\)	\(e\left(\frac{7}{39}\right)\)