Dirichlet character \(\chi_{1375}(862,\cdot)\)

• Label: 1375.862
• Modulus: $1375$
• Conductor: $1375$
• Order: $100$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1375\)
Conductor:	\(1375\)
Order:	\(100\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1375.cs

\(\chi_{1375}(37,\cdot)\) \(\chi_{1375}(53,\cdot)\) \(\chi_{1375}(97,\cdot)\) \(\chi_{1375}(102,\cdot)\) \(\chi_{1375}(192,\cdot)\) \(\chi_{1375}(213,\cdot)\) \(\chi_{1375}(223,\cdot)\) \(\chi_{1375}(258,\cdot)\) \(\chi_{1375}(312,\cdot)\) \(\chi_{1375}(328,\cdot)\) \(\chi_{1375}(372,\cdot)\) \(\chi_{1375}(377,\cdot)\) \(\chi_{1375}(467,\cdot)\) \(\chi_{1375}(488,\cdot)\) \(\chi_{1375}(498,\cdot)\) \(\chi_{1375}(533,\cdot)\) \(\chi_{1375}(587,\cdot)\) \(\chi_{1375}(603,\cdot)\) \(\chi_{1375}(647,\cdot)\) \(\chi_{1375}(652,\cdot)\) \(\chi_{1375}(742,\cdot)\) \(\chi_{1375}(763,\cdot)\) \(\chi_{1375}(773,\cdot)\) \(\chi_{1375}(808,\cdot)\) \(\chi_{1375}(862,\cdot)\) \(\chi_{1375}(878,\cdot)\) \(\chi_{1375}(922,\cdot)\) \(\chi_{1375}(927,\cdot)\) \(\chi_{1375}(1017,\cdot)\) \(\chi_{1375}(1038,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{100})$
Fixed field:	Number field defined by a degree 100 polynomial

Values on generators

\((1002,376)\) → \((e\left(\frac{89}{100}\right),e\left(\frac{1}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1375 }(862, a) \)	\(-1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)