Dirichlet character χ2509(1010,⋅)\chi_{2509}(1010,\cdot)

• Label: 2509.1010
• Modulus: $2509$
• Conductor: $2509$
• Order: $192$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2509$
Conductor:	$2509$
Order:	$192$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2509.ep

$\chi_{2509}(22,\cdot)$ $\chi_{2509}(146,\cdot)$ $\chi_{2509}(152,\cdot)$ $\chi_{2509}(159,\cdot)$ $\chi_{2509}(178,\cdot)$ $\chi_{2509}(237,\cdot)$ $\chi_{2509}(308,\cdot)$ $\chi_{2509}(360,\cdot)$ $\chi_{2509}(412,\cdot)$ $\chi_{2509}(464,\cdot)$ $\chi_{2509}(497,\cdot)$ $\chi_{2509}(549,\cdot)$ $\chi_{2509}(594,\cdot)$ $\chi_{2509}(620,\cdot)$ $\chi_{2509}(640,\cdot)$ $\chi_{2509}(692,\cdot)$ $\chi_{2509}(750,\cdot)$ $\chi_{2509}(789,\cdot)$ $\chi_{2509}(809,\cdot)$ $\chi_{2509}(874,\cdot)$ $\chi_{2509}(913,\cdot)$ $\chi_{2509}(984,\cdot)$ $\chi_{2509}(1010,\cdot)$ $\chi_{2509}(1017,\cdot)$ $\chi_{2509}(1023,\cdot)$ $\chi_{2509}(1056,\cdot)$ $\chi_{2509}(1088,\cdot)$ $\chi_{2509}(1101,\cdot)$ $\chi_{2509}(1121,\cdot)$ $\chi_{2509}(1153,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{192})$
Fixed field:	Number field defined by a degree 192 polynomial (not computed)

Values on generators

$(1159,391)$ → $(e\left(\frac{2}{3}\right),e\left(\frac{169}{192}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 2509 }(1010, a)$	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{143}{192}\right)$