Dirichlet character χ4598(251,⋅)\chi_{4598}(251,\cdot)

• Label: 4598.251
• Modulus: $4598$
• Conductor: $209$
• Order: $45$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$4598$
Conductor:	$209$
Order:	$45$
Real:	no
Primitive:	no, induced from $\chi_{209}(42,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 4598.z

$\chi_{4598}(9,\cdot)$ $\chi_{4598}(81,\cdot)$ $\chi_{4598}(245,\cdot)$ $\chi_{4598}(251,\cdot)$ $\chi_{4598}(511,\cdot)$ $\chi_{4598}(807,\cdot)$ $\chi_{4598}(1049,\cdot)$ $\chi_{4598}(1213,\cdot)$ $\chi_{4598}(1461,\cdot)$ $\chi_{4598}(1479,\cdot)$ $\chi_{4598}(1697,\cdot)$ $\chi_{4598}(1963,\cdot)$ $\chi_{4598}(2259,\cdot)$ $\chi_{4598}(2429,\cdot)$ $\chi_{4598}(2665,\cdot)$ $\chi_{4598}(2913,\cdot)$ $\chi_{4598}(2931,\cdot)$ $\chi_{4598}(3227,\cdot)$ $\chi_{4598}(3391,\cdot)$ $\chi_{4598}(3633,\cdot)$ $\chi_{4598}(3657,\cdot)$ $\chi_{4598}(3711,\cdot)$ $\chi_{4598}(3881,\cdot)$ $\chi_{4598}(3899,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1

Values on generators

$(3269,3631)$ → $(e\left(\frac{3}{5}\right),e\left(\frac{1}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{ 4598 }(251, a)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{45}\right)$