Dirichlet character χ3872(1839,⋅)\chi_{3872}(1839,\cdot)

• Label: 3872.1839
• Modulus: $3872$
• Conductor: $968$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$3872$
Conductor:	$968$
Order:	$110$
Real:	no
Primitive:	no, induced from $\chi_{968}(387,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 3872.by

$\chi_{3872}(79,\cdot)$ $\chi_{3872}(271,\cdot)$ $\chi_{3872}(303,\cdot)$ $\chi_{3872}(431,\cdot)$ $\chi_{3872}(591,\cdot)$ $\chi_{3872}(623,\cdot)$ $\chi_{3872}(655,\cdot)$ $\chi_{3872}(783,\cdot)$ $\chi_{3872}(943,\cdot)$ $\chi_{3872}(975,\cdot)$ $\chi_{3872}(1007,\cdot)$ $\chi_{3872}(1135,\cdot)$ $\chi_{3872}(1295,\cdot)$ $\chi_{3872}(1327,\cdot)$ $\chi_{3872}(1359,\cdot)$ $\chi_{3872}(1487,\cdot)$ $\chi_{3872}(1647,\cdot)$ $\chi_{3872}(1679,\cdot)$ $\chi_{3872}(1711,\cdot)$ $\chi_{3872}(1839,\cdot)$ $\chi_{3872}(1999,\cdot)$ $\chi_{3872}(2031,\cdot)$ $\chi_{3872}(2063,\cdot)$ $\chi_{3872}(2191,\cdot)$ $\chi_{3872}(2351,\cdot)$ $\chi_{3872}(2383,\cdot)$ $\chi_{3872}(2415,\cdot)$ $\chi_{3872}(2543,\cdot)$ $\chi_{3872}(2703,\cdot)$ $\chi_{3872}(2735,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

$(1695,485,2785)$ → $(-1,-1,e\left(\frac{91}{110}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 3872 }(1839, a)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$