Dirichlet character \(\chi_{8415}(367,\cdot)\)

• Label: 8415.367
• Modulus: $8415$
• Conductor: $8415$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8415\)
Conductor:	\(8415\)
Order:	\(240\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8415.kp

\(\chi_{8415}(148,\cdot)\) \(\chi_{8415}(328,\cdot)\) \(\chi_{8415}(367,\cdot)\) \(\chi_{8415}(598,\cdot)\) \(\chi_{8415}(643,\cdot)\) \(\chi_{8415}(652,\cdot)\) \(\chi_{8415}(742,\cdot)\) \(\chi_{8415}(907,\cdot)\) \(\chi_{8415}(1093,\cdot)\) \(\chi_{8415}(1417,\cdot)\) \(\chi_{8415}(1642,\cdot)\) \(\chi_{8415}(1897,\cdot)\) \(\chi_{8415}(2128,\cdot)\) \(\chi_{8415}(2182,\cdot)\) \(\chi_{8415}(2302,\cdot)\) \(\chi_{8415}(2407,\cdot)\) \(\chi_{8415}(2623,\cdot)\) \(\chi_{8415}(2698,\cdot)\) \(\chi_{8415}(3067,\cdot)\) \(\chi_{8415}(3172,\cdot)\) \(\chi_{8415}(3193,\cdot)\) \(\chi_{8415}(3292,\cdot)\) \(\chi_{8415}(3463,\cdot)\) \(\chi_{8415}(3712,\cdot)\) \(\chi_{8415}(3832,\cdot)\) \(\chi_{8415}(3958,\cdot)\) \(\chi_{8415}(4057,\cdot)\) \(\chi_{8415}(4228,\cdot)\) \(\chi_{8415}(4678,\cdot)\) \(\chi_{8415}(4702,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

Values on generators

\((7481,3367,1531,496)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{1}{5}\right),e\left(\frac{3}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(19\)	\(23\)	\(26\)
\( \chi_{ 8415 }(367, a) \)	\(1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{31}{40}\right)\)