Dirichlet character χ201(50,⋅)\chi_{201}(50,\cdot)

• Label: 201.50
• Modulus: $201$
• Conductor: $201$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$201$
Conductor:	$201$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 201.p

$\chi_{201}(2,\cdot)$ $\chi_{201}(11,\cdot)$ $\chi_{201}(20,\cdot)$ $\chi_{201}(32,\cdot)$ $\chi_{201}(41,\cdot)$ $\chi_{201}(44,\cdot)$ $\chi_{201}(50,\cdot)$ $\chi_{201}(74,\cdot)$ $\chi_{201}(80,\cdot)$ $\chi_{201}(95,\cdot)$ $\chi_{201}(98,\cdot)$ $\chi_{201}(101,\cdot)$ $\chi_{201}(113,\cdot)$ $\chi_{201}(128,\cdot)$ $\chi_{201}(146,\cdot)$ $\chi_{201}(152,\cdot)$ $\chi_{201}(182,\cdot)$ $\chi_{201}(185,\cdot)$ $\chi_{201}(191,\cdot)$ $\chi_{201}(197,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(68,136)$ → $(-1,e\left(\frac{31}{66}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 201 }(50, a)$	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{29}{33}\right)$

Gauss sum

Jacobi sum

Kloosterman sum