Dirichlet character χ704(59,⋅)\chi_{704}(59,\cdot)

• Label: 704.59
• Modulus: $704$
• Conductor: $704$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$704$
Conductor:	$704$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 704.bl

$\chi_{704}(3,\cdot)$ $\chi_{704}(27,\cdot)$ $\chi_{704}(59,\cdot)$ $\chi_{704}(75,\cdot)$ $\chi_{704}(91,\cdot)$ $\chi_{704}(115,\cdot)$ $\chi_{704}(147,\cdot)$ $\chi_{704}(163,\cdot)$ $\chi_{704}(179,\cdot)$ $\chi_{704}(203,\cdot)$ $\chi_{704}(235,\cdot)$ $\chi_{704}(251,\cdot)$ $\chi_{704}(267,\cdot)$ $\chi_{704}(291,\cdot)$ $\chi_{704}(323,\cdot)$ $\chi_{704}(339,\cdot)$ $\chi_{704}(355,\cdot)$ $\chi_{704}(379,\cdot)$ $\chi_{704}(411,\cdot)$ $\chi_{704}(427,\cdot)$ $\chi_{704}(443,\cdot)$ $\chi_{704}(467,\cdot)$ $\chi_{704}(499,\cdot)$ $\chi_{704}(515,\cdot)$ $\chi_{704}(531,\cdot)$ $\chi_{704}(555,\cdot)$ $\chi_{704}(587,\cdot)$ $\chi_{704}(603,\cdot)$ $\chi_{704}(619,\cdot)$ $\chi_{704}(643,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

$(639,133,321)$ → $(-1,e\left(\frac{1}{16}\right),e\left(\frac{1}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 704 }(59, a)$	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$

Gauss sum

Jacobi sum

Kloosterman sum