Dirichlet character \(\chi_{10700}(4191,\cdot)\)

• Label: 10700.4191
• Modulus: $10700$
• Conductor: $10700$
• Order: $530$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(10700\)
Conductor:	\(10700\)
Order:	\(530\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 10700.bl

\(\chi_{10700}(31,\cdot)\) \(\chi_{10700}(71,\cdot)\) \(\chi_{10700}(91,\cdot)\) \(\chi_{10700}(131,\cdot)\) \(\chi_{10700}(191,\cdot)\) \(\chi_{10700}(211,\cdot)\) \(\chi_{10700}(231,\cdot)\) \(\chi_{10700}(291,\cdot)\) \(\chi_{10700}(311,\cdot)\) \(\chi_{10700}(371,\cdot)\) \(\chi_{10700}(391,\cdot)\) \(\chi_{10700}(471,\cdot)\) \(\chi_{10700}(491,\cdot)\) \(\chi_{10700}(531,\cdot)\) \(\chi_{10700}(631,\cdot)\) \(\chi_{10700}(771,\cdot)\) \(\chi_{10700}(831,\cdot)\) \(\chi_{10700}(871,\cdot)\) \(\chi_{10700}(911,\cdot)\) \(\chi_{10700}(971,\cdot)\) \(\chi_{10700}(991,\cdot)\) \(\chi_{10700}(1031,\cdot)\) \(\chi_{10700}(1091,\cdot)\) \(\chi_{10700}(1231,\cdot)\) \(\chi_{10700}(1271,\cdot)\) \(\chi_{10700}(1291,\cdot)\) \(\chi_{10700}(1411,\cdot)\) \(\chi_{10700}(1471,\cdot)\) \(\chi_{10700}(1571,\cdot)\) \(\chi_{10700}(1591,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{265})$
Fixed field:	Number field defined by a degree 530 polynomial (not computed)

Values on generators

\((5351,7277,6101)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{35}{106}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 10700 }(4191, a) \)	\(1\)	\(1\)	\(e\left(\frac{7}{530}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{7}{265}\right)\)	\(e\left(\frac{511}{530}\right)\)	\(e\left(\frac{112}{265}\right)\)	\(e\left(\frac{93}{530}\right)\)	\(e\left(\frac{453}{530}\right)\)	\(e\left(\frac{377}{530}\right)\)	\(e\left(\frac{91}{530}\right)\)	\(e\left(\frac{21}{530}\right)\)