Dirichlet character χ3600(3413,⋅)\chi_{3600}(3413,\cdot)

• Label: 3600.3413
• Modulus: $3600$
• Conductor: $3600$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3600$
Conductor:	$3600$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3600.fv

$\chi_{3600}(77,\cdot)$ $\chi_{3600}(317,\cdot)$ $\chi_{3600}(533,\cdot)$ $\chi_{3600}(797,\cdot)$ $\chi_{3600}(1013,\cdot)$ $\chi_{3600}(1037,\cdot)$ $\chi_{3600}(1253,\cdot)$ $\chi_{3600}(1517,\cdot)$ $\chi_{3600}(1733,\cdot)$ $\chi_{3600}(1973,\cdot)$ $\chi_{3600}(2237,\cdot)$ $\chi_{3600}(2453,\cdot)$ $\chi_{3600}(2477,\cdot)$ $\chi_{3600}(3173,\cdot)$ $\chi_{3600}(3197,\cdot)$ $\chi_{3600}(3413,\cdot)$

Related number fields

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

Values on generators

$(3151,901,2801,577)$ → $(1,i,e\left(\frac{1}{6}\right),e\left(\frac{19}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 3600 }(3413, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$