Dirichlet character \(\chi_{4693}(1013,\cdot)\)

• Label: 4693.1013
• Modulus: $4693$
• Conductor: $4693$
• Order: $342$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4693\)
Conductor:	\(4693\)
Order:	\(342\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4693.df

\(\chi_{4693}(25,\cdot)\) \(\chi_{4693}(142,\cdot)\) \(\chi_{4693}(168,\cdot)\) \(\chi_{4693}(194,\cdot)\) \(\chi_{4693}(207,\cdot)\) \(\chi_{4693}(233,\cdot)\) \(\chi_{4693}(272,\cdot)\) \(\chi_{4693}(441,\cdot)\) \(\chi_{4693}(454,\cdot)\) \(\chi_{4693}(480,\cdot)\) \(\chi_{4693}(519,\cdot)\) \(\chi_{4693}(636,\cdot)\) \(\chi_{4693}(662,\cdot)\) \(\chi_{4693}(688,\cdot)\) \(\chi_{4693}(701,\cdot)\) \(\chi_{4693}(727,\cdot)\) \(\chi_{4693}(766,\cdot)\) \(\chi_{4693}(883,\cdot)\) \(\chi_{4693}(909,\cdot)\) \(\chi_{4693}(935,\cdot)\) \(\chi_{4693}(948,\cdot)\) \(\chi_{4693}(974,\cdot)\) \(\chi_{4693}(1013,\cdot)\) \(\chi_{4693}(1130,\cdot)\) \(\chi_{4693}(1156,\cdot)\) \(\chi_{4693}(1195,\cdot)\) \(\chi_{4693}(1221,\cdot)\) \(\chi_{4693}(1260,\cdot)\) \(\chi_{4693}(1377,\cdot)\) \(\chi_{4693}(1403,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

Values on generators

\((1445,3251)\) → \((-1,e\left(\frac{106}{171}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4693 }(1013, a) \)	\(1\)	\(1\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)