Dirichlet character χ700(37,⋅)\chi_{700}(37,\cdot)

• Label: 700.37
• Modulus: $700$
• Conductor: $175$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$700$
Conductor:	$175$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{175}(37,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 700.bu

$\chi_{700}(37,\cdot)$ $\chi_{700}(53,\cdot)$ $\chi_{700}(137,\cdot)$ $\chi_{700}(177,\cdot)$ $\chi_{700}(233,\cdot)$ $\chi_{700}(277,\cdot)$ $\chi_{700}(317,\cdot)$ $\chi_{700}(333,\cdot)$ $\chi_{700}(373,\cdot)$ $\chi_{700}(417,\cdot)$ $\chi_{700}(473,\cdot)$ $\chi_{700}(513,\cdot)$ $\chi_{700}(597,\cdot)$ $\chi_{700}(613,\cdot)$ $\chi_{700}(653,\cdot)$ $\chi_{700}(697,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(351,477,101)$ → $(1,e\left(\frac{9}{20}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{ 700 }(37, a)$	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$

Gauss sum

Jacobi sum

Kloosterman sum