Dirichlet character χ441(110,⋅)\chi_{441}(110,\cdot)

• Label: 441.110
• Modulus: $441$
• Conductor: $441$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$441$
Conductor:	$441$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 441.bd

$\chi_{441}(47,\cdot)$ $\chi_{441}(59,\cdot)$ $\chi_{441}(110,\cdot)$ $\chi_{441}(122,\cdot)$ $\chi_{441}(173,\cdot)$ $\chi_{441}(185,\cdot)$ $\chi_{441}(236,\cdot)$ $\chi_{441}(248,\cdot)$ $\chi_{441}(299,\cdot)$ $\chi_{441}(311,\cdot)$ $\chi_{441}(425,\cdot)$ $\chi_{441}(437,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(344,199)$ → $(e\left(\frac{1}{6}\right),e\left(\frac{11}{42}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 441 }(110, a)$	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum