Dirichlet character χ4650(3707,⋅)\chi_{4650}(3707,\cdot)

• Label: 4650.3707
• Modulus: $4650$
• Conductor: $465$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4650$
Conductor:	$465$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{465}(452,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4650.fs

$\chi_{4650}(107,\cdot)$ $\chi_{4650}(143,\cdot)$ $\chi_{4650}(257,\cdot)$ $\chi_{4650}(293,\cdot)$ $\chi_{4650}(443,\cdot)$ $\chi_{4650}(857,\cdot)$ $\chi_{4650}(1043,\cdot)$ $\chi_{4650}(1157,\cdot)$ $\chi_{4650}(1343,\cdot)$ $\chi_{4650}(3107,\cdot)$ $\chi_{4650}(3293,\cdot)$ $\chi_{4650}(3407,\cdot)$ $\chi_{4650}(3593,\cdot)$ $\chi_{4650}(3707,\cdot)$ $\chi_{4650}(3893,\cdot)$ $\chi_{4650}(4607,\cdot)$

Related number fields

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

Values on generators

$(3101,2977,1801)$ → $(-1,i,e\left(\frac{13}{15}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$37$	$41$	$43$
$\chi_{ 4650 }(3707, a)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{60}\right)$