Dirichlet character χ3040(1403,⋅)\chi_{3040}(1403,\cdot)

• Label: 3040.1403
• 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.gk

$\chi_{3040}(43,\cdot)$ $\chi_{3040}(123,\cdot)$ $\chi_{3040}(283,\cdot)$ $\chi_{3040}(443,\cdot)$ $\chi_{3040}(707,\cdot)$ $\chi_{3040}(947,\cdot)$ $\chi_{3040}(1107,\cdot)$ $\chi_{3040}(1163,\cdot)$ $\chi_{3040}(1187,\cdot)$ $\chi_{3040}(1347,\cdot)$ $\chi_{3040}(1403,\cdot)$ $\chi_{3040}(1507,\cdot)$ $\chi_{3040}(1563,\cdot)$ $\chi_{3040}(1643,\cdot)$ $\chi_{3040}(1803,\cdot)$ $\chi_{3040}(1963,\cdot)$ $\chi_{3040}(2227,\cdot)$ $\chi_{3040}(2467,\cdot)$ $\chi_{3040}(2627,\cdot)$ $\chi_{3040}(2683,\cdot)$ $\chi_{3040}(2707,\cdot)$ $\chi_{3040}(2867,\cdot)$ $\chi_{3040}(2923,\cdot)$ $\chi_{3040}(3027,\cdot)$

Related number fields

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

Values on generators

$(191,2661,1217,1921)$ → $(-1,e\left(\frac{1}{8}\right),-i,e\left(\frac{2}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3040 }(1403, a)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{72}\right)$