Dirichlet character \(\chi_{14700}(8963,\cdot)\)

• Label: 14700.8963
• Modulus: $14700$
• Conductor: $14700$
• Order: $420$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(14700\)
Conductor:	\(14700\)
Order:	\(420\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 14700.hd

\(\chi_{14700}(47,\cdot)\) \(\chi_{14700}(383,\cdot)\) \(\chi_{14700}(467,\cdot)\) \(\chi_{14700}(563,\cdot)\) \(\chi_{14700}(647,\cdot)\) \(\chi_{14700}(887,\cdot)\) \(\chi_{14700}(983,\cdot)\) \(\chi_{14700}(1067,\cdot)\) \(\chi_{14700}(1223,\cdot)\) \(\chi_{14700}(1487,\cdot)\) \(\chi_{14700}(1727,\cdot)\) \(\chi_{14700}(1823,\cdot)\) \(\chi_{14700}(2063,\cdot)\) \(\chi_{14700}(2147,\cdot)\) \(\chi_{14700}(2327,\cdot)\) \(\chi_{14700}(2483,\cdot)\) \(\chi_{14700}(2663,\cdot)\) \(\chi_{14700}(2747,\cdot)\) \(\chi_{14700}(2903,\cdot)\) \(\chi_{14700}(2987,\cdot)\) \(\chi_{14700}(3083,\cdot)\) \(\chi_{14700}(3323,\cdot)\) \(\chi_{14700}(3503,\cdot)\) \(\chi_{14700}(3587,\cdot)\) \(\chi_{14700}(3827,\cdot)\) \(\chi_{14700}(3923,\cdot)\) \(\chi_{14700}(4163,\cdot)\) \(\chi_{14700}(4247,\cdot)\) \(\chi_{14700}(4427,\cdot)\) \(\chi_{14700}(4583,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

\((7351,4901,1177,9901)\) → \((-1,-1,e\left(\frac{19}{20}\right),e\left(\frac{31}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 14700 }(8963, a) \)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)