Dirichlet character χ4140(53,⋅)\chi_{4140}(53,\cdot)

• Label: 4140.53
• Modulus: $4140$
• Conductor: $345$
• Order: $44$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$4140$
Conductor:	$345$
Order:	$44$
Real:	no
Primitive:	no, induced from $\chi_{345}(53,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 4140.cn

$\chi_{4140}(17,\cdot)$ $\chi_{4140}(53,\cdot)$ $\chi_{4140}(557,\cdot)$ $\chi_{4140}(773,\cdot)$ $\chi_{4140}(917,\cdot)$ $\chi_{4140}(953,\cdot)$ $\chi_{4140}(1493,\cdot)$ $\chi_{4140}(1673,\cdot)$ $\chi_{4140}(1997,\cdot)$ $\chi_{4140}(2177,\cdot)$ $\chi_{4140}(2213,\cdot)$ $\chi_{4140}(2357,\cdot)$ $\chi_{4140}(2537,\cdot)$ $\chi_{4140}(2573,\cdot)$ $\chi_{4140}(3257,\cdot)$ $\chi_{4140}(3437,\cdot)$ $\chi_{4140}(3653,\cdot)$ $\chi_{4140}(3833,\cdot)$ $\chi_{4140}(3977,\cdot)$ $\chi_{4140}(4013,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{44})$
Fixed field:	Number field defined by a degree 44 polynomial

Values on generators

$(2071,461,1657,3961)$ → $(1,-1,-i,e\left(\frac{19}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(53, a)$	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$