Dirichlet character \(\chi_{9025}(37,\cdot)\)

• Label: 9025.37
• Modulus: $9025$
• Conductor: $9025$
• Order: $380$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(9025\)
Conductor:	\(9025\)
Order:	\(380\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 9025.cg

\(\chi_{9025}(37,\cdot)\) \(\chi_{9025}(113,\cdot)\) \(\chi_{9025}(208,\cdot)\) \(\chi_{9025}(227,\cdot)\) \(\chi_{9025}(303,\cdot)\) \(\chi_{9025}(322,\cdot)\) \(\chi_{9025}(398,\cdot)\) \(\chi_{9025}(417,\cdot)\) \(\chi_{9025}(512,\cdot)\) \(\chi_{9025}(588,\cdot)\) \(\chi_{9025}(683,\cdot)\) \(\chi_{9025}(702,\cdot)\) \(\chi_{9025}(778,\cdot)\) \(\chi_{9025}(797,\cdot)\) \(\chi_{9025}(873,\cdot)\) \(\chi_{9025}(892,\cdot)\) \(\chi_{9025}(987,\cdot)\) \(\chi_{9025}(1063,\cdot)\) \(\chi_{9025}(1158,\cdot)\) \(\chi_{9025}(1177,\cdot)\) \(\chi_{9025}(1253,\cdot)\) \(\chi_{9025}(1272,\cdot)\) \(\chi_{9025}(1348,\cdot)\) \(\chi_{9025}(1367,\cdot)\) \(\chi_{9025}(1462,\cdot)\) \(\chi_{9025}(1538,\cdot)\) \(\chi_{9025}(1633,\cdot)\) \(\chi_{9025}(1652,\cdot)\) \(\chi_{9025}(1728,\cdot)\) \(\chi_{9025}(1747,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{380})$
Fixed field:	Number field defined by a degree 380 polynomial (not computed)

Values on generators

\((5777,3251)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{5}{38}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 9025 }(37, a) \)	\(1\)	\(1\)	\(e\left(\frac{221}{380}\right)\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{31}{190}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{229}{380}\right)\)	\(e\left(\frac{319}{380}\right)\)