Dirichlet character \(\chi_{2527}(563,\cdot)\)

• Label: 2527.563
• Modulus: $2527$
• Conductor: $2527$
• Order: $114$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2527\)
Conductor:	\(2527\)
Order:	\(114\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2527.bp

\(\chi_{2527}(31,\cdot)\) \(\chi_{2527}(103,\cdot)\) \(\chi_{2527}(164,\cdot)\) \(\chi_{2527}(236,\cdot)\) \(\chi_{2527}(297,\cdot)\) \(\chi_{2527}(369,\cdot)\) \(\chi_{2527}(502,\cdot)\) \(\chi_{2527}(563,\cdot)\) \(\chi_{2527}(635,\cdot)\) \(\chi_{2527}(696,\cdot)\) \(\chi_{2527}(768,\cdot)\) \(\chi_{2527}(829,\cdot)\) \(\chi_{2527}(901,\cdot)\) \(\chi_{2527}(962,\cdot)\) \(\chi_{2527}(1034,\cdot)\) \(\chi_{2527}(1095,\cdot)\) \(\chi_{2527}(1167,\cdot)\) \(\chi_{2527}(1228,\cdot)\) \(\chi_{2527}(1300,\cdot)\) \(\chi_{2527}(1361,\cdot)\) \(\chi_{2527}(1433,\cdot)\) \(\chi_{2527}(1494,\cdot)\) \(\chi_{2527}(1566,\cdot)\) \(\chi_{2527}(1627,\cdot)\) \(\chi_{2527}(1699,\cdot)\) \(\chi_{2527}(1760,\cdot)\) \(\chi_{2527}(1832,\cdot)\) \(\chi_{2527}(1893,\cdot)\) \(\chi_{2527}(1965,\cdot)\) \(\chi_{2527}(2026,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 114 polynomial (not computed)

Values on generators

\((1445,1807)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{114}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 2527 }(563, a) \)	\(1\)	\(1\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)