Dirichlet character χ46208(37,⋅)\chi_{46208}(37,\cdot)

• Label: 46208.37
• Modulus: $46208$
• Conductor: $46208$
• Order: $608$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$46208$
Conductor:	$46208$
Order:	$608$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 46208.eo

$\chi_{46208}(37,\cdot)$ $\chi_{46208}(189,\cdot)$ $\chi_{46208}(341,\cdot)$ $\chi_{46208}(493,\cdot)$ $\chi_{46208}(645,\cdot)$ $\chi_{46208}(797,\cdot)$ $\chi_{46208}(949,\cdot)$ $\chi_{46208}(1101,\cdot)$ $\chi_{46208}(1253,\cdot)$ $\chi_{46208}(1405,\cdot)$ $\chi_{46208}(1557,\cdot)$ $\chi_{46208}(1709,\cdot)$ $\chi_{46208}(1861,\cdot)$ $\chi_{46208}(2013,\cdot)$ $\chi_{46208}(2317,\cdot)$ $\chi_{46208}(2469,\cdot)$ $\chi_{46208}(2621,\cdot)$ $\chi_{46208}(2773,\cdot)$ $\chi_{46208}(2925,\cdot)$ $\chi_{46208}(3077,\cdot)$ $\chi_{46208}(3229,\cdot)$ $\chi_{46208}(3381,\cdot)$ $\chi_{46208}(3533,\cdot)$ $\chi_{46208}(3685,\cdot)$ $\chi_{46208}(3837,\cdot)$ $\chi_{46208}(3989,\cdot)$ $\chi_{46208}(4141,\cdot)$ $\chi_{46208}(4293,\cdot)$ $\chi_{46208}(4445,\cdot)$ $\chi_{46208}(4597,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{608})$
Fixed field:	Number field defined by a degree 608 polynomial (not computed)

Values on generators

$(28159,36101,14081)$ → $(1,e\left(\frac{25}{32}\right),e\left(\frac{5}{38}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{ 46208 }(37, a)$	$-1$	$1$	$e\left(\frac{385}{608}\right)$	$e\left(\frac{187}{608}\right)$	$e\left(\frac{167}{304}\right)$	$e\left(\frac{81}{304}\right)$	$e\left(\frac{503}{608}\right)$	$e\left(\frac{5}{608}\right)$	$e\left(\frac{143}{152}\right)$	$e\left(\frac{93}{152}\right)$	$e\left(\frac{111}{608}\right)$	$e\left(\frac{45}{304}\right)$