Dirichlet character χ3600(817,⋅)\chi_{3600}(817,\cdot)

• Label: 3600.817
• Modulus: $3600$
• Conductor: $225$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$3600$
Conductor:	$225$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{225}(142,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 3600.fy

$\chi_{3600}(97,\cdot)$ $\chi_{3600}(337,\cdot)$ $\chi_{3600}(673,\cdot)$ $\chi_{3600}(817,\cdot)$ $\chi_{3600}(913,\cdot)$ $\chi_{3600}(1537,\cdot)$ $\chi_{3600}(1633,\cdot)$ $\chi_{3600}(1777,\cdot)$ $\chi_{3600}(2113,\cdot)$ $\chi_{3600}(2353,\cdot)$ $\chi_{3600}(2497,\cdot)$ $\chi_{3600}(2833,\cdot)$ $\chi_{3600}(2977,\cdot)$ $\chi_{3600}(3073,\cdot)$ $\chi_{3600}(3217,\cdot)$ $\chi_{3600}(3553,\cdot)$

Related number fields

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

Values on generators

$(3151,901,2801,577)$ → $(1,1,e\left(\frac{2}{3}\right),e\left(\frac{13}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 3600 }(817, a)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$