Dirichlet character \(\chi_{7225}(2089,\cdot)\)

• Label: 7225.2089
• Modulus: $7225$
• Conductor: $7225$
• Order: $680$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(7225\)
Conductor:	\(7225\)
Order:	\(680\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 7225.co

\(\chi_{7225}(9,\cdot)\) \(\chi_{7225}(19,\cdot)\) \(\chi_{7225}(59,\cdot)\) \(\chi_{7225}(94,\cdot)\) \(\chi_{7225}(104,\cdot)\) \(\chi_{7225}(144,\cdot)\) \(\chi_{7225}(189,\cdot)\) \(\chi_{7225}(219,\cdot)\) \(\chi_{7225}(229,\cdot)\) \(\chi_{7225}(264,\cdot)\) \(\chi_{7225}(304,\cdot)\) \(\chi_{7225}(314,\cdot)\) \(\chi_{7225}(359,\cdot)\) \(\chi_{7225}(389,\cdot)\) \(\chi_{7225}(434,\cdot)\) \(\chi_{7225}(484,\cdot)\) \(\chi_{7225}(519,\cdot)\) \(\chi_{7225}(529,\cdot)\) \(\chi_{7225}(559,\cdot)\) \(\chi_{7225}(569,\cdot)\) \(\chi_{7225}(604,\cdot)\) \(\chi_{7225}(614,\cdot)\) \(\chi_{7225}(644,\cdot)\) \(\chi_{7225}(654,\cdot)\) \(\chi_{7225}(689,\cdot)\) \(\chi_{7225}(729,\cdot)\) \(\chi_{7225}(739,\cdot)\) \(\chi_{7225}(784,\cdot)\) \(\chi_{7225}(814,\cdot)\) \(\chi_{7225}(859,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{680})$
Fixed field:	Number field defined by a degree 680 polynomial (not computed)

Values on generators

\((2602,2026)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{107}{136}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 7225 }(2089, a) \)	\(1\)	\(1\)	\(e\left(\frac{267}{340}\right)\)	\(e\left(\frac{603}{680}\right)\)	\(e\left(\frac{97}{170}\right)\)	\(e\left(\frac{457}{680}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{121}{340}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{609}{680}\right)\)	\(e\left(\frac{311}{680}\right)\)	\(e\left(\frac{77}{85}\right)\)