Dirichlet character \(\chi_{1225}(12,\cdot)\)

• Label: 1225.12
• Modulus: $1225$
• Conductor: $1225$
• Order: $420$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1225\)
Conductor:	\(1225\)
Order:	\(420\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1225.bu

\(\chi_{1225}(3,\cdot)\) \(\chi_{1225}(12,\cdot)\) \(\chi_{1225}(17,\cdot)\) \(\chi_{1225}(33,\cdot)\) \(\chi_{1225}(38,\cdot)\) \(\chi_{1225}(47,\cdot)\) \(\chi_{1225}(52,\cdot)\) \(\chi_{1225}(73,\cdot)\) \(\chi_{1225}(87,\cdot)\) \(\chi_{1225}(103,\cdot)\) \(\chi_{1225}(108,\cdot)\) \(\chi_{1225}(122,\cdot)\) \(\chi_{1225}(138,\cdot)\) \(\chi_{1225}(152,\cdot)\) \(\chi_{1225}(173,\cdot)\) \(\chi_{1225}(187,\cdot)\) \(\chi_{1225}(192,\cdot)\) \(\chi_{1225}(208,\cdot)\) \(\chi_{1225}(213,\cdot)\) \(\chi_{1225}(222,\cdot)\) \(\chi_{1225}(248,\cdot)\) \(\chi_{1225}(262,\cdot)\) \(\chi_{1225}(278,\cdot)\) \(\chi_{1225}(283,\cdot)\) \(\chi_{1225}(292,\cdot)\) \(\chi_{1225}(297,\cdot)\) \(\chi_{1225}(327,\cdot)\) \(\chi_{1225}(348,\cdot)\) \(\chi_{1225}(353,\cdot)\) \(\chi_{1225}(367,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

\((1177,101)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{11}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\( \chi_{ 1225 }(12, a) \)	\(1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{4}{105}\right)\)