Dirichlet character \(\chi_{15840}(1597,\cdot)\)

• Label: 15840.1597
• Modulus: $15840$
• Conductor: $15840$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(15840\)
Conductor:	\(15840\)
Order:	\(120\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 15840.qc

\(\chi_{15840}(853,\cdot)\) \(\chi_{15840}(877,\cdot)\) \(\chi_{15840}(1597,\cdot)\) \(\chi_{15840}(2317,\cdot)\) \(\chi_{15840}(3253,\cdot)\) \(\chi_{15840}(3517,\cdot)\) \(\chi_{15840}(3757,\cdot)\) \(\chi_{15840}(3973,\cdot)\) \(\chi_{15840}(4237,\cdot)\) \(\chi_{15840}(4693,\cdot)\) \(\chi_{15840}(4957,\cdot)\) \(\chi_{15840}(5893,\cdot)\) \(\chi_{15840}(6133,\cdot)\) \(\chi_{15840}(6397,\cdot)\) \(\chi_{15840}(6613,\cdot)\) \(\chi_{15840}(7333,\cdot)\) \(\chi_{15840}(8773,\cdot)\) \(\chi_{15840}(8797,\cdot)\) \(\chi_{15840}(9517,\cdot)\) \(\chi_{15840}(10237,\cdot)\) \(\chi_{15840}(11173,\cdot)\) \(\chi_{15840}(11437,\cdot)\) \(\chi_{15840}(11677,\cdot)\) \(\chi_{15840}(11893,\cdot)\) \(\chi_{15840}(12157,\cdot)\) \(\chi_{15840}(12613,\cdot)\) \(\chi_{15840}(12877,\cdot)\) \(\chi_{15840}(13813,\cdot)\) \(\chi_{15840}(14053,\cdot)\) \(\chi_{15840}(14317,\cdot)\) ...

Related number fields

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

Values on generators

\((991,13861,3521,6337,14401)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{1}{3}\right),i,e\left(\frac{1}{10}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 15840 }(1597, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)