Dirichlet character \(\chi_{1573}(1033,\cdot)\)

• Label: 1573.1033
• Modulus: $1573$
• Conductor: $1573$
• Order: $132$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1573\)
Conductor:	\(1573\)
Order:	\(132\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1573.bn

\(\chi_{1573}(32,\cdot)\) \(\chi_{1573}(54,\cdot)\) \(\chi_{1573}(76,\cdot)\) \(\chi_{1573}(98,\cdot)\) \(\chi_{1573}(175,\cdot)\) \(\chi_{1573}(197,\cdot)\) \(\chi_{1573}(219,\cdot)\) \(\chi_{1573}(318,\cdot)\) \(\chi_{1573}(340,\cdot)\) \(\chi_{1573}(384,\cdot)\) \(\chi_{1573}(461,\cdot)\) \(\chi_{1573}(505,\cdot)\) \(\chi_{1573}(527,\cdot)\) \(\chi_{1573}(626,\cdot)\) \(\chi_{1573}(648,\cdot)\) \(\chi_{1573}(670,\cdot)\) \(\chi_{1573}(747,\cdot)\) \(\chi_{1573}(769,\cdot)\) \(\chi_{1573}(791,\cdot)\) \(\chi_{1573}(813,\cdot)\) \(\chi_{1573}(890,\cdot)\) \(\chi_{1573}(912,\cdot)\) \(\chi_{1573}(934,\cdot)\) \(\chi_{1573}(956,\cdot)\) \(\chi_{1573}(1033,\cdot)\) \(\chi_{1573}(1055,\cdot)\) \(\chi_{1573}(1077,\cdot)\) \(\chi_{1573}(1099,\cdot)\) \(\chi_{1573}(1176,\cdot)\) \(\chi_{1573}(1198,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

Values on generators

\((365,1211)\) → \((e\left(\frac{13}{22}\right),e\left(\frac{5}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 1573 }(1033, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)