Dirichlet character \(\chi_{3648}(515,\cdot)\)

• Label: 3648.515
• Modulus: $3648$
• Conductor: $3648$
• Order: $144$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(3648\)
Conductor:	\(3648\)
Order:	\(144\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3648.em

\(\chi_{3648}(59,\cdot)\) \(\chi_{3648}(155,\cdot)\) \(\chi_{3648}(203,\cdot)\) \(\chi_{3648}(299,\cdot)\) \(\chi_{3648}(371,\cdot)\) \(\chi_{3648}(395,\cdot)\) \(\chi_{3648}(515,\cdot)\) \(\chi_{3648}(611,\cdot)\) \(\chi_{3648}(659,\cdot)\) \(\chi_{3648}(755,\cdot)\) \(\chi_{3648}(827,\cdot)\) \(\chi_{3648}(851,\cdot)\) \(\chi_{3648}(971,\cdot)\) \(\chi_{3648}(1067,\cdot)\) \(\chi_{3648}(1115,\cdot)\) \(\chi_{3648}(1211,\cdot)\) \(\chi_{3648}(1283,\cdot)\) \(\chi_{3648}(1307,\cdot)\) \(\chi_{3648}(1427,\cdot)\) \(\chi_{3648}(1523,\cdot)\) \(\chi_{3648}(1571,\cdot)\) \(\chi_{3648}(1667,\cdot)\) \(\chi_{3648}(1739,\cdot)\) \(\chi_{3648}(1763,\cdot)\) \(\chi_{3648}(1883,\cdot)\) \(\chi_{3648}(1979,\cdot)\) \(\chi_{3648}(2027,\cdot)\) \(\chi_{3648}(2123,\cdot)\) \(\chi_{3648}(2195,\cdot)\) \(\chi_{3648}(2219,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

Values on generators

\((2623,2053,1217,1921)\) → \((-1,e\left(\frac{3}{16}\right),-1,e\left(\frac{1}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 3648 }(515, a) \)	\(-1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{144}\right)\)