Dirichlet character χ4598(65,⋅)\chi_{4598}(65,\cdot)

• Label: 4598.65
• Modulus: $4598$
• Conductor: $2299$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4598$
Conductor:	$2299$
Order:	$66$
Real:	no
Primitive:	no, induced from $\chi_{2299}(65,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4598.bd

$\chi_{4598}(65,\cdot)$ $\chi_{4598}(373,\cdot)$ $\chi_{4598}(791,\cdot)$ $\chi_{4598}(901,\cdot)$ $\chi_{4598}(1319,\cdot)$ $\chi_{4598}(1627,\cdot)$ $\chi_{4598}(1737,\cdot)$ $\chi_{4598}(2045,\cdot)$ $\chi_{4598}(2155,\cdot)$ $\chi_{4598}(2463,\cdot)$ $\chi_{4598}(2573,\cdot)$ $\chi_{4598}(2881,\cdot)$ $\chi_{4598}(2991,\cdot)$ $\chi_{4598}(3299,\cdot)$ $\chi_{4598}(3409,\cdot)$ $\chi_{4598}(3717,\cdot)$ $\chi_{4598}(3827,\cdot)$ $\chi_{4598}(4135,\cdot)$ $\chi_{4598}(4245,\cdot)$ $\chi_{4598}(4553,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(3269,3631)$ → $(e\left(\frac{13}{22}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{ 4598 }(65, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{26}{33}\right)$