Dirichlet character χ4650(173,⋅)\chi_{4650}(173,\cdot)

• Label: 4650.173
• Modulus: $4650$
• Conductor: $2325$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4650$
Conductor:	$2325$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{2325}(173,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4650.fx

$\chi_{4650}(173,\cdot)$ $\chi_{4650}(317,\cdot)$ $\chi_{4650}(413,\cdot)$ $\chi_{4650}(887,\cdot)$ $\chi_{4650}(1433,\cdot)$ $\chi_{4650}(2087,\cdot)$ $\chi_{4650}(2153,\cdot)$ $\chi_{4650}(2303,\cdot)$ $\chi_{4650}(2477,\cdot)$ $\chi_{4650}(2717,\cdot)$ $\chi_{4650}(2777,\cdot)$ $\chi_{4650}(2897,\cdot)$ $\chi_{4650}(3047,\cdot)$ $\chi_{4650}(3833,\cdot)$ $\chi_{4650}(3863,\cdot)$ $\chi_{4650}(4523,\cdot)$

Related number fields

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

Values on generators

$(3101,2977,1801)$ → $(-1,e\left(\frac{11}{20}\right),e\left(\frac{13}{15}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$37$	$41$	$43$
$\chi_{ 4650 }(173, a)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{60}\right)$