Dirichlet character \(\chi_{4225}(413,\cdot)\)

• Label: 4225.413
• Modulus: $4225$
• Conductor: $4225$
• Order: $780$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(4225\)
Conductor:	\(4225\)
Order:	\(780\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 4225.cz

\(\chi_{4225}(17,\cdot)\) \(\chi_{4225}(62,\cdot)\) \(\chi_{4225}(88,\cdot)\) \(\chi_{4225}(108,\cdot)\) \(\chi_{4225}(127,\cdot)\) \(\chi_{4225}(153,\cdot)\) \(\chi_{4225}(173,\cdot)\) \(\chi_{4225}(212,\cdot)\) \(\chi_{4225}(238,\cdot)\) \(\chi_{4225}(277,\cdot)\) \(\chi_{4225}(283,\cdot)\) \(\chi_{4225}(303,\cdot)\) \(\chi_{4225}(322,\cdot)\) \(\chi_{4225}(342,\cdot)\) \(\chi_{4225}(348,\cdot)\) \(\chi_{4225}(387,\cdot)\) \(\chi_{4225}(413,\cdot)\) \(\chi_{4225}(433,\cdot)\) \(\chi_{4225}(452,\cdot)\) \(\chi_{4225}(472,\cdot)\) \(\chi_{4225}(478,\cdot)\) \(\chi_{4225}(498,\cdot)\) \(\chi_{4225}(517,\cdot)\) \(\chi_{4225}(537,\cdot)\) \(\chi_{4225}(563,\cdot)\) \(\chi_{4225}(602,\cdot)\) \(\chi_{4225}(608,\cdot)\) \(\chi_{4225}(628,\cdot)\) \(\chi_{4225}(647,\cdot)\) \(\chi_{4225}(667,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{780})$
Fixed field:	Number field defined by a degree 780 polynomial (not computed)

Values on generators

\((677,3551)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{71}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\( \chi_{ 4225 }(413, a) \)	\(-1\)	\(1\)	\(e\left(\frac{671}{780}\right)\)	\(e\left(\frac{407}{780}\right)\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{149}{390}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{17}{390}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{1}{130}\right)\)