Dirichlet character \(\chi_{632}(397,\cdot)\)

• Label: 632.397
• Modulus: $632$
• Conductor: $632$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(632\)
Conductor:	\(632\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 632.z

\(\chi_{632}(5,\cdot)\) \(\chi_{632}(13,\cdot)\) \(\chi_{632}(45,\cdot)\) \(\chi_{632}(189,\cdot)\) \(\chi_{632}(253,\cdot)\) \(\chi_{632}(269,\cdot)\) \(\chi_{632}(277,\cdot)\) \(\chi_{632}(309,\cdot)\) \(\chi_{632}(325,\cdot)\) \(\chi_{632}(341,\cdot)\) \(\chi_{632}(365,\cdot)\) \(\chi_{632}(389,\cdot)\) \(\chi_{632}(397,\cdot)\) \(\chi_{632}(421,\cdot)\) \(\chi_{632}(437,\cdot)\) \(\chi_{632}(445,\cdot)\) \(\chi_{632}(485,\cdot)\) \(\chi_{632}(493,\cdot)\) \(\chi_{632}(525,\cdot)\) \(\chi_{632}(557,\cdot)\) \(\chi_{632}(573,\cdot)\) \(\chi_{632}(589,\cdot)\) \(\chi_{632}(597,\cdot)\) \(\chi_{632}(629,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((159,317,161)\) → \((1,-1,e\left(\frac{2}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 632 }(397, a) \)	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum