Dirichlet character χ608(299,⋅)\chi_{608}(299,\cdot)

• Label: 608.299
• Modulus: $608$
• Conductor: $608$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$608$
Conductor:	$608$
Order:	$72$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 608.bt

$\chi_{608}(3,\cdot)$ $\chi_{608}(51,\cdot)$ $\chi_{608}(59,\cdot)$ $\chi_{608}(67,\cdot)$ $\chi_{608}(91,\cdot)$ $\chi_{608}(147,\cdot)$ $\chi_{608}(155,\cdot)$ $\chi_{608}(203,\cdot)$ $\chi_{608}(211,\cdot)$ $\chi_{608}(219,\cdot)$ $\chi_{608}(243,\cdot)$ $\chi_{608}(299,\cdot)$ $\chi_{608}(307,\cdot)$ $\chi_{608}(355,\cdot)$ $\chi_{608}(363,\cdot)$ $\chi_{608}(371,\cdot)$ $\chi_{608}(395,\cdot)$ $\chi_{608}(451,\cdot)$ $\chi_{608}(459,\cdot)$ $\chi_{608}(507,\cdot)$ $\chi_{608}(515,\cdot)$ $\chi_{608}(523,\cdot)$ $\chi_{608}(547,\cdot)$ $\chi_{608}(603,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

$(191,229,97)$ → $(-1,e\left(\frac{5}{8}\right),e\left(\frac{7}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{ 608 }(299, a)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{36}\right)$

Gauss sum

Jacobi sum

Kloosterman sum