Dirichlet character \(\chi_{14700}(5531,\cdot)\)

• Label: 14700.5531
• Modulus: $14700$
• Conductor: $14700$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(14700\)
Conductor:	\(14700\)
Order:	\(70\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 14700.fu

\(\chi_{14700}(71,\cdot)\) \(\chi_{14700}(911,\cdot)\) \(\chi_{14700}(1331,\cdot)\) \(\chi_{14700}(2171,\cdot)\) \(\chi_{14700}(2591,\cdot)\) \(\chi_{14700}(3011,\cdot)\) \(\chi_{14700}(4271,\cdot)\) \(\chi_{14700}(4691,\cdot)\) \(\chi_{14700}(5111,\cdot)\) \(\chi_{14700}(5531,\cdot)\) \(\chi_{14700}(6791,\cdot)\) \(\chi_{14700}(7211,\cdot)\) \(\chi_{14700}(7631,\cdot)\) \(\chi_{14700}(8471,\cdot)\) \(\chi_{14700}(8891,\cdot)\) \(\chi_{14700}(9731,\cdot)\) \(\chi_{14700}(10571,\cdot)\) \(\chi_{14700}(10991,\cdot)\) \(\chi_{14700}(11411,\cdot)\) \(\chi_{14700}(11831,\cdot)\) \(\chi_{14700}(12671,\cdot)\) \(\chi_{14700}(13091,\cdot)\) \(\chi_{14700}(13511,\cdot)\) \(\chi_{14700}(13931,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Values on generators

\((7351,4901,1177,9901)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 14700 }(5531, a) \)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)