Dirichlet character χ4598(31,⋅)\chi_{4598}(31,\cdot)

• Label: 4598.31
• Modulus: $4598$
• Conductor: $2299$
• Order: $330$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$4598$
Conductor:	$2299$
Order:	$330$
Real:	no
Primitive:	no, induced from $\chi_{2299}(31,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 4598.bq

$\chi_{4598}(31,\cdot)$ $\chi_{4598}(69,\cdot)$ $\chi_{4598}(103,\cdot)$ $\chi_{4598}(141,\cdot)$ $\chi_{4598}(179,\cdot)$ $\chi_{4598}(335,\cdot)$ $\chi_{4598}(411,\cdot)$ $\chi_{4598}(445,\cdot)$ $\chi_{4598}(449,\cdot)$ $\chi_{4598}(521,\cdot)$ $\chi_{4598}(559,\cdot)$ $\chi_{4598}(597,\cdot)$ $\chi_{4598}(829,\cdot)$ $\chi_{4598}(863,\cdot)$ $\chi_{4598}(867,\cdot)$ $\chi_{4598}(905,\cdot)$ $\chi_{4598}(939,\cdot)$ $\chi_{4598}(1015,\cdot)$ $\chi_{4598}(1171,\cdot)$ $\chi_{4598}(1247,\cdot)$ $\chi_{4598}(1281,\cdot)$ $\chi_{4598}(1285,\cdot)$ $\chi_{4598}(1323,\cdot)$ $\chi_{4598}(1357,\cdot)$ $\chi_{4598}(1395,\cdot)$ $\chi_{4598}(1433,\cdot)$ $\chi_{4598}(1589,\cdot)$ $\chi_{4598}(1665,\cdot)$ $\chi_{4598}(1699,\cdot)$ $\chi_{4598}(1741,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

$(3269,3631)$ → $(e\left(\frac{43}{55}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{ 4598 }(31, a)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{62}{165}\right)$