Dirichlet character χ1309(41,⋅)\chi_{1309}(41,\cdot)

• Label: 1309.41
• Modulus: $1309$
• Conductor: $1309$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1309$
Conductor:	$1309$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1309.cs

$\chi_{1309}(6,\cdot)$ $\chi_{1309}(41,\cdot)$ $\chi_{1309}(62,\cdot)$ $\chi_{1309}(90,\cdot)$ $\chi_{1309}(139,\cdot)$ $\chi_{1309}(160,\cdot)$ $\chi_{1309}(167,\cdot)$ $\chi_{1309}(216,\cdot)$ $\chi_{1309}(244,\cdot)$ $\chi_{1309}(398,\cdot)$ $\chi_{1309}(447,\cdot)$ $\chi_{1309}(503,\cdot)$ $\chi_{1309}(524,\cdot)$ $\chi_{1309}(601,\cdot)$ $\chi_{1309}(622,\cdot)$ $\chi_{1309}(657,\cdot)$ $\chi_{1309}(734,\cdot)$ $\chi_{1309}(755,\cdot)$ $\chi_{1309}(776,\cdot)$ $\chi_{1309}(811,\cdot)$ $\chi_{1309}(853,\cdot)$ $\chi_{1309}(860,\cdot)$ $\chi_{1309}(930,\cdot)$ $\chi_{1309}(1014,\cdot)$ $\chi_{1309}(1042,\cdot)$ $\chi_{1309}(1091,\cdot)$ $\chi_{1309}(1119,\cdot)$ $\chi_{1309}(1161,\cdot)$ $\chi_{1309}(1168,\cdot)$ $\chi_{1309}(1196,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

$(1123,596,309)$ → $(-1,e\left(\frac{3}{10}\right),e\left(\frac{11}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 1309 }(41, a)$	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{20}\right)$