Dirichlet character \(\chi_{1573}(1010,\cdot)\)

• Label: 1573.1010
• Modulus: $1573$
• Conductor: $1573$
• Order: $165$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1573\)
Conductor:	\(1573\)
Order:	\(165\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1573.bo

\(\chi_{1573}(16,\cdot)\) \(\chi_{1573}(42,\cdot)\) \(\chi_{1573}(48,\cdot)\) \(\chi_{1573}(113,\cdot)\) \(\chi_{1573}(126,\cdot)\) \(\chi_{1573}(146,\cdot)\) \(\chi_{1573}(152,\cdot)\) \(\chi_{1573}(159,\cdot)\) \(\chi_{1573}(185,\cdot)\) \(\chi_{1573}(191,\cdot)\) \(\chi_{1573}(224,\cdot)\) \(\chi_{1573}(256,\cdot)\) \(\chi_{1573}(289,\cdot)\) \(\chi_{1573}(295,\cdot)\) \(\chi_{1573}(302,\cdot)\) \(\chi_{1573}(328,\cdot)\) \(\chi_{1573}(334,\cdot)\) \(\chi_{1573}(367,\cdot)\) \(\chi_{1573}(399,\cdot)\) \(\chi_{1573}(412,\cdot)\) \(\chi_{1573}(432,\cdot)\) \(\chi_{1573}(438,\cdot)\) \(\chi_{1573}(445,\cdot)\) \(\chi_{1573}(471,\cdot)\) \(\chi_{1573}(477,\cdot)\) \(\chi_{1573}(510,\cdot)\) \(\chi_{1573}(542,\cdot)\) \(\chi_{1573}(555,\cdot)\) \(\chi_{1573}(575,\cdot)\) \(\chi_{1573}(581,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 165 polynomial (not computed)

Values on generators

\((365,1211)\) → \((e\left(\frac{48}{55}\right),e\left(\frac{2}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 1573 }(1010, a) \)	\(1\)	\(1\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)