Dirichlet character \(\chi_{14700}(83,\cdot)\)

• Label: 14700.83
• Modulus: $14700$
• Conductor: $14700$
• Order: $140$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(14700\)
Conductor:	\(14700\)
Order:	\(140\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 14700.gm

\(\chi_{14700}(83,\cdot)\) \(\chi_{14700}(167,\cdot)\) \(\chi_{14700}(503,\cdot)\) \(\chi_{14700}(923,\cdot)\) \(\chi_{14700}(1427,\cdot)\) \(\chi_{14700}(1847,\cdot)\) \(\chi_{14700}(2183,\cdot)\) \(\chi_{14700}(2267,\cdot)\) \(\chi_{14700}(2603,\cdot)\) \(\chi_{14700}(2687,\cdot)\) \(\chi_{14700}(3023,\cdot)\) \(\chi_{14700}(3863,\cdot)\) \(\chi_{14700}(3947,\cdot)\) \(\chi_{14700}(4283,\cdot)\) \(\chi_{14700}(4367,\cdot)\) \(\chi_{14700}(4787,\cdot)\) \(\chi_{14700}(5123,\cdot)\) \(\chi_{14700}(5627,\cdot)\) \(\chi_{14700}(5963,\cdot)\) \(\chi_{14700}(6047,\cdot)\) \(\chi_{14700}(6383,\cdot)\) \(\chi_{14700}(6803,\cdot)\) \(\chi_{14700}(6887,\cdot)\) \(\chi_{14700}(7223,\cdot)\) \(\chi_{14700}(7727,\cdot)\) \(\chi_{14700}(8063,\cdot)\) \(\chi_{14700}(8147,\cdot)\) \(\chi_{14700}(8483,\cdot)\) \(\chi_{14700}(8567,\cdot)\) \(\chi_{14700}(8903,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{140})$
Fixed field:	Number field defined by a degree 140 polynomial (not computed)

Values on generators

\((7351,4901,1177,9901)\) → \((-1,-1,e\left(\frac{3}{20}\right),e\left(\frac{3}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 14700 }(83, a) \)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)