Dirichlet character χ735(53,⋅)\chi_{735}(53,\cdot)

• Label: 735.53
• Modulus: $735$
• Conductor: $735$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$735$
Conductor:	$735$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 735.bt

$\chi_{735}(2,\cdot)$ $\chi_{735}(23,\cdot)$ $\chi_{735}(32,\cdot)$ $\chi_{735}(53,\cdot)$ $\chi_{735}(107,\cdot)$ $\chi_{735}(137,\cdot)$ $\chi_{735}(158,\cdot)$ $\chi_{735}(212,\cdot)$ $\chi_{735}(233,\cdot)$ $\chi_{735}(242,\cdot)$ $\chi_{735}(317,\cdot)$ $\chi_{735}(338,\cdot)$ $\chi_{735}(347,\cdot)$ $\chi_{735}(368,\cdot)$ $\chi_{735}(443,\cdot)$ $\chi_{735}(452,\cdot)$ $\chi_{735}(473,\cdot)$ $\chi_{735}(527,\cdot)$ $\chi_{735}(548,\cdot)$ $\chi_{735}(578,\cdot)$ $\chi_{735}(632,\cdot)$ $\chi_{735}(653,\cdot)$ $\chi_{735}(662,\cdot)$ $\chi_{735}(683,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(491,442,346)$ → $(-1,-i,e\left(\frac{5}{21}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 735 }(53, a)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{67}{84}\right)$

Gauss sum

Jacobi sum

Kloosterman sum