Dirichlet character \(\chi_{2025}(47,\cdot)\)

• Label: 2025.47
• Modulus: $2025$
• Conductor: $2025$
• Order: $540$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2025\)
Conductor:	\(2025\)
Order:	\(540\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2025.bv

\(\chi_{2025}(2,\cdot)\) \(\chi_{2025}(23,\cdot)\) \(\chi_{2025}(38,\cdot)\) \(\chi_{2025}(47,\cdot)\) \(\chi_{2025}(77,\cdot)\) \(\chi_{2025}(83,\cdot)\) \(\chi_{2025}(92,\cdot)\) \(\chi_{2025}(113,\cdot)\) \(\chi_{2025}(122,\cdot)\) \(\chi_{2025}(128,\cdot)\) \(\chi_{2025}(137,\cdot)\) \(\chi_{2025}(158,\cdot)\) \(\chi_{2025}(167,\cdot)\) \(\chi_{2025}(173,\cdot)\) \(\chi_{2025}(203,\cdot)\) \(\chi_{2025}(212,\cdot)\) \(\chi_{2025}(227,\cdot)\) \(\chi_{2025}(248,\cdot)\) \(\chi_{2025}(263,\cdot)\) \(\chi_{2025}(272,\cdot)\) \(\chi_{2025}(302,\cdot)\) \(\chi_{2025}(308,\cdot)\) \(\chi_{2025}(317,\cdot)\) \(\chi_{2025}(338,\cdot)\) \(\chi_{2025}(347,\cdot)\) \(\chi_{2025}(353,\cdot)\) \(\chi_{2025}(362,\cdot)\) \(\chi_{2025}(383,\cdot)\) \(\chi_{2025}(392,\cdot)\) \(\chi_{2025}(398,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{540})$
Fixed field:	Number field defined by a degree 540 polynomial (not computed)

Values on generators

\((326,1702)\) → \((e\left(\frac{7}{54}\right),e\left(\frac{17}{20}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 2025 }(47, a) \)	\(1\)	\(1\)	\(e\left(\frac{529}{540}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{101}{540}\right)\)	\(e\left(\frac{41}{135}\right)\)	\(e\left(\frac{124}{135}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)