Dirichlet character \(\chi_{407}(157,\cdot)\)

• Label: 407.157
• Modulus: $407$
• Conductor: $407$
• Order: $45$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(407\)
Conductor:	\(407\)
Order:	\(45\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 407.bc

\(\chi_{407}(9,\cdot)\) \(\chi_{407}(16,\cdot)\) \(\chi_{407}(49,\cdot)\) \(\chi_{407}(53,\cdot)\) \(\chi_{407}(70,\cdot)\) \(\chi_{407}(71,\cdot)\) \(\chi_{407}(81,\cdot)\) \(\chi_{407}(86,\cdot)\) \(\chi_{407}(108,\cdot)\) \(\chi_{407}(157,\cdot)\) \(\chi_{407}(181,\cdot)\) \(\chi_{407}(192,\cdot)\) \(\chi_{407}(201,\cdot)\) \(\chi_{407}(218,\cdot)\) \(\chi_{407}(229,\cdot)\) \(\chi_{407}(234,\cdot)\) \(\chi_{407}(256,\cdot)\) \(\chi_{407}(268,\cdot)\) \(\chi_{407}(312,\cdot)\) \(\chi_{407}(345,\cdot)\) \(\chi_{407}(366,\cdot)\) \(\chi_{407}(367,\cdot)\) \(\chi_{407}(377,\cdot)\) \(\chi_{407}(379,\cdot)\)

Related number fields

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

Values on generators

\((112,298)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{4}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 407 }(157, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum