Dirichlet character \(\chi_{1225}(348,\cdot)\)

• Label: 1225.348
• 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

\((1177,101)\) → \((e\left(\frac{11}{20}\right),e\left(\frac{29}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\( \chi_{ 1225 }(348, a) \)	\(1\)	\(1\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{1}{105}\right)\)