Dirichlet character \(\chi_{8415}(7924,\cdot)\)

• Label: 8415.7924
• Modulus: $8415$
• Conductor: $8415$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8415\)
Conductor:	\(8415\)
Order:	\(120\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8415.kh

\(\chi_{8415}(49,\cdot)\) \(\chi_{8415}(229,\cdot)\) \(\chi_{8415}(994,\cdot)\) \(\chi_{8415}(1039,\cdot)\) \(\chi_{8415}(1114,\cdot)\) \(\chi_{8415}(1879,\cdot)\) \(\chi_{8415}(2524,\cdot)\) \(\chi_{8415}(2599,\cdot)\) \(\chi_{8415}(2644,\cdot)\) \(\chi_{8415}(3364,\cdot)\) \(\chi_{8415}(3589,\cdot)\) \(\chi_{8415}(3919,\cdot)\) \(\chi_{8415}(4129,\cdot)\) \(\chi_{8415}(4174,\cdot)\) \(\chi_{8415}(4354,\cdot)\) \(\chi_{8415}(4684,\cdot)\) \(\chi_{8415}(5074,\cdot)\) \(\chi_{8415}(5119,\cdot)\) \(\chi_{8415}(5404,\cdot)\) \(\chi_{8415}(5449,\cdot)\) \(\chi_{8415}(5659,\cdot)\) \(\chi_{8415}(5839,\cdot)\) \(\chi_{8415}(6169,\cdot)\) \(\chi_{8415}(6394,\cdot)\) \(\chi_{8415}(6604,\cdot)\) \(\chi_{8415}(6649,\cdot)\) \(\chi_{8415}(6934,\cdot)\) \(\chi_{8415}(6979,\cdot)\) \(\chi_{8415}(7159,\cdot)\) \(\chi_{8415}(7879,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((7481,3367,1531,496)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{1}{5}\right),e\left(\frac{7}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(19\)	\(23\)	\(26\)
\( \chi_{ 8415 }(7924, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{20}\right)\)