Dirichlet character χ3040(1573,⋅)\chi_{3040}(1573,\cdot)

• Label: 3040.1573
• 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.fy

$\chi_{3040}(53,\cdot)$ $\chi_{3040}(317,\cdot)$ $\chi_{3040}(477,\cdot)$ $\chi_{3040}(637,\cdot)$ $\chi_{3040}(717,\cdot)$ $\chi_{3040}(773,\cdot)$ $\chi_{3040}(877,\cdot)$ $\chi_{3040}(933,\cdot)$ $\chi_{3040}(1093,\cdot)$ $\chi_{3040}(1117,\cdot)$ $\chi_{3040}(1173,\cdot)$ $\chi_{3040}(1333,\cdot)$ $\chi_{3040}(1573,\cdot)$ $\chi_{3040}(1837,\cdot)$ $\chi_{3040}(1997,\cdot)$ $\chi_{3040}(2157,\cdot)$ $\chi_{3040}(2237,\cdot)$ $\chi_{3040}(2293,\cdot)$ $\chi_{3040}(2397,\cdot)$ $\chi_{3040}(2453,\cdot)$ $\chi_{3040}(2613,\cdot)$ $\chi_{3040}(2637,\cdot)$ $\chi_{3040}(2693,\cdot)$ $\chi_{3040}(2853,\cdot)$

Related number fields

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

Values on generators

$(191,2661,1217,1921)$ → $(1,e\left(\frac{1}{8}\right),-i,e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3040 }(1573, a)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{72}\right)$