Dirichlet character \(\chi_{1225}(554,\cdot)\)

• Label: 1225.554
• Modulus: $1225$
• Conductor: $1225$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1225\)
Conductor:	\(1225\)
Order:	\(70\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1225.bj

\(\chi_{1225}(29,\cdot)\) \(\chi_{1225}(64,\cdot)\) \(\chi_{1225}(134,\cdot)\) \(\chi_{1225}(169,\cdot)\) \(\chi_{1225}(204,\cdot)\) \(\chi_{1225}(239,\cdot)\) \(\chi_{1225}(309,\cdot)\) \(\chi_{1225}(379,\cdot)\) \(\chi_{1225}(414,\cdot)\) \(\chi_{1225}(484,\cdot)\) \(\chi_{1225}(519,\cdot)\) \(\chi_{1225}(554,\cdot)\) \(\chi_{1225}(659,\cdot)\) \(\chi_{1225}(694,\cdot)\) \(\chi_{1225}(729,\cdot)\) \(\chi_{1225}(764,\cdot)\) \(\chi_{1225}(869,\cdot)\) \(\chi_{1225}(904,\cdot)\) \(\chi_{1225}(939,\cdot)\) \(\chi_{1225}(1009,\cdot)\) \(\chi_{1225}(1044,\cdot)\) \(\chi_{1225}(1114,\cdot)\) \(\chi_{1225}(1184,\cdot)\) \(\chi_{1225}(1219,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Values on generators

\((1177,101)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{5}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\( \chi_{ 1225 }(554, a) \)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)