Dirichlet character χ3040(1397,⋅)\chi_{3040}(1397,\cdot)

• Label: 3040.1397
• Modulus: $3040$
• Conductor: $3040$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3040$
Conductor:	$3040$
Order:	$72$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3040.gl

$\chi_{3040}(13,\cdot)$ $\chi_{3040}(117,\cdot)$ $\chi_{3040}(173,\cdot)$ $\chi_{3040}(333,\cdot)$ $\chi_{3040}(357,\cdot)$ $\chi_{3040}(413,\cdot)$ $\chi_{3040}(573,\cdot)$ $\chi_{3040}(813,\cdot)$ $\chi_{3040}(1077,\cdot)$ $\chi_{3040}(1237,\cdot)$ $\chi_{3040}(1397,\cdot)$ $\chi_{3040}(1477,\cdot)$ $\chi_{3040}(1533,\cdot)$ $\chi_{3040}(1637,\cdot)$ $\chi_{3040}(1693,\cdot)$ $\chi_{3040}(1853,\cdot)$ $\chi_{3040}(1877,\cdot)$ $\chi_{3040}(1933,\cdot)$ $\chi_{3040}(2093,\cdot)$ $\chi_{3040}(2333,\cdot)$ $\chi_{3040}(2597,\cdot)$ $\chi_{3040}(2757,\cdot)$ $\chi_{3040}(2917,\cdot)$ $\chi_{3040}(2997,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

$(191,2661,1217,1921)$ → $(1,e\left(\frac{5}{8}\right),i,e\left(\frac{17}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3040 }(1397, a)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{72}\right)$