Dirichlet character χ296(35,⋅)\chi_{296}(35,\cdot)

• Label: 296.35
• Modulus: $296$
• Conductor: $296$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$296$
Conductor:	$296$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 296.bj

$\chi_{296}(19,\cdot)$ $\chi_{296}(35,\cdot)$ $\chi_{296}(59,\cdot)$ $\chi_{296}(91,\cdot)$ $\chi_{296}(131,\cdot)$ $\chi_{296}(163,\cdot)$ $\chi_{296}(187,\cdot)$ $\chi_{296}(203,\cdot)$ $\chi_{296}(227,\cdot)$ $\chi_{296}(235,\cdot)$ $\chi_{296}(283,\cdot)$ $\chi_{296}(291,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.36.138892919952333446776057851184385905517238171566853781889085447929331712.1

Values on generators

$(223,149,113)$ → $(-1,-1,e\left(\frac{19}{36}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 296 }(35, a)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum