Dirichlet character χ3040(149,⋅)\chi_{3040}(149,\cdot)

• Label: 3040.149
• 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.gc

$\chi_{3040}(149,\cdot)$ $\chi_{3040}(309,\cdot)$ $\chi_{3040}(389,\cdot)$ $\chi_{3040}(549,\cdot)$ $\chi_{3040}(669,\cdot)$ $\chi_{3040}(709,\cdot)$ $\chi_{3040}(909,\cdot)$ $\chi_{3040}(1069,\cdot)$ $\chi_{3040}(1149,\cdot)$ $\chi_{3040}(1309,\cdot)$ $\chi_{3040}(1429,\cdot)$ $\chi_{3040}(1469,\cdot)$ $\chi_{3040}(1669,\cdot)$ $\chi_{3040}(1829,\cdot)$ $\chi_{3040}(1909,\cdot)$ $\chi_{3040}(2069,\cdot)$ $\chi_{3040}(2189,\cdot)$ $\chi_{3040}(2229,\cdot)$ $\chi_{3040}(2429,\cdot)$ $\chi_{3040}(2589,\cdot)$ $\chi_{3040}(2669,\cdot)$ $\chi_{3040}(2829,\cdot)$ $\chi_{3040}(2949,\cdot)$ $\chi_{3040}(2989,\cdot)$

Related number fields

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

Values on generators

$(191,2661,1217,1921)$ → $(1,e\left(\frac{5}{8}\right),-1,e\left(\frac{2}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3040 }(149, a)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{47}{72}\right)$