Dirichlet character χ920(517,⋅)\chi_{920}(517,\cdot)

• Label: 920.517
• Modulus: $920$
• Conductor: $920$
• Order: $44$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$920$
Conductor:	$920$
Order:	$44$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 920.bo

$\chi_{920}(37,\cdot)$ $\chi_{920}(53,\cdot)$ $\chi_{920}(157,\cdot)$ $\chi_{920}(237,\cdot)$ $\chi_{920}(293,\cdot)$ $\chi_{920}(333,\cdot)$ $\chi_{920}(373,\cdot)$ $\chi_{920}(477,\cdot)$ $\chi_{920}(493,\cdot)$ $\chi_{920}(517,\cdot)$ $\chi_{920}(557,\cdot)$ $\chi_{920}(573,\cdot)$ $\chi_{920}(613,\cdot)$ $\chi_{920}(677,\cdot)$ $\chi_{920}(733,\cdot)$ $\chi_{920}(757,\cdot)$ $\chi_{920}(773,\cdot)$ $\chi_{920}(797,\cdot)$ $\chi_{920}(893,\cdot)$ $\chi_{920}(917,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{44})$
Fixed field:	44.44.13383169230192059253459701104387771124501004765020501667165784506368000000000000000000000000000000000.1

Values on generators

$(231,461,737,281)$ → $(1,-1,i,e\left(\frac{9}{22}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{ 920 }(517, a)$	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum