Dirichlet character χ2704(633,⋅)\chi_{2704}(633,\cdot)

• Label: 2704.633
• Modulus: $2704$
• Conductor: $1352$
• Order: $78$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$2704$
Conductor:	$1352$
Order:	$78$
Real:	no
Primitive:	no, induced from $\chi_{1352}(1309,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 2704.cl

$\chi_{2704}(9,\cdot)$ $\chi_{2704}(185,\cdot)$ $\chi_{2704}(217,\cdot)$ $\chi_{2704}(393,\cdot)$ $\chi_{2704}(425,\cdot)$ $\chi_{2704}(601,\cdot)$ $\chi_{2704}(633,\cdot)$ $\chi_{2704}(809,\cdot)$ $\chi_{2704}(841,\cdot)$ $\chi_{2704}(1017,\cdot)$ $\chi_{2704}(1049,\cdot)$ $\chi_{2704}(1225,\cdot)$ $\chi_{2704}(1257,\cdot)$ $\chi_{2704}(1433,\cdot)$ $\chi_{2704}(1465,\cdot)$ $\chi_{2704}(1641,\cdot)$ $\chi_{2704}(1673,\cdot)$ $\chi_{2704}(1849,\cdot)$ $\chi_{2704}(2057,\cdot)$ $\chi_{2704}(2089,\cdot)$ $\chi_{2704}(2265,\cdot)$ $\chi_{2704}(2297,\cdot)$ $\chi_{2704}(2473,\cdot)$ $\chi_{2704}(2505,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

$(2367,677,1185)$ → $(1,-1,e\left(\frac{11}{39}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 2704 }(633, a)$	$1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{3}\right)$