Dirichlet character \(\chi_{407}(141,\cdot)\)

• Label: 407.141
• Modulus: $407$
• Conductor: $407$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(407\)
Conductor:	\(407\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 407.bg

\(\chi_{407}(3,\cdot)\) \(\chi_{407}(4,\cdot)\) \(\chi_{407}(25,\cdot)\) \(\chi_{407}(58,\cdot)\) \(\chi_{407}(102,\cdot)\) \(\chi_{407}(104,\cdot)\) \(\chi_{407}(114,\cdot)\) \(\chi_{407}(115,\cdot)\) \(\chi_{407}(136,\cdot)\) \(\chi_{407}(141,\cdot)\) \(\chi_{407}(152,\cdot)\) \(\chi_{407}(169,\cdot)\) \(\chi_{407}(213,\cdot)\) \(\chi_{407}(225,\cdot)\) \(\chi_{407}(247,\cdot)\) \(\chi_{407}(262,\cdot)\) \(\chi_{407}(280,\cdot)\) \(\chi_{407}(284,\cdot)\) \(\chi_{407}(289,\cdot)\) \(\chi_{407}(300,\cdot)\) \(\chi_{407}(317,\cdot)\) \(\chi_{407}(324,\cdot)\) \(\chi_{407}(361,\cdot)\) \(\chi_{407}(400,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

\((112,298)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 407 }(141, a) \)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum