Dirichlet character χ736(617,⋅)\chi_{736}(617,\cdot)

• Label: 736.617
• Modulus: $736$
• Conductor: $368$
• Order: $44$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$736$
Conductor:	$368$
Order:	$44$
Real:	no
Primitive:	no, induced from $\chi_{368}(157,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 736.z

$\chi_{736}(57,\cdot)$ $\chi_{736}(89,\cdot)$ $\chi_{736}(153,\cdot)$ $\chi_{736}(201,\cdot)$ $\chi_{736}(217,\cdot)$ $\chi_{736}(249,\cdot)$ $\chi_{736}(281,\cdot)$ $\chi_{736}(297,\cdot)$ $\chi_{736}(313,\cdot)$ $\chi_{736}(329,\cdot)$ $\chi_{736}(425,\cdot)$ $\chi_{736}(457,\cdot)$ $\chi_{736}(521,\cdot)$ $\chi_{736}(569,\cdot)$ $\chi_{736}(585,\cdot)$ $\chi_{736}(617,\cdot)$ $\chi_{736}(649,\cdot)$ $\chi_{736}(665,\cdot)$ $\chi_{736}(681,\cdot)$ $\chi_{736}(697,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{44})$
Fixed field:	44.0.4141890260646712580912980965306954513336276372715662057543551492310346739946349214617837764608.1

Values on generators

$(415,645,97)$ → $(1,-i,e\left(\frac{15}{22}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 736 }(617, a)$	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{27}{44}\right)$

Gauss sum

Jacobi sum

Kloosterman sum