Dirichlet character χ8788(389,⋅)\chi_{8788}(389,\cdot)

• Label: 8788.389
• Modulus: $8788$
• Conductor: $2197$
• Order: $338$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8788$
Conductor:	$2197$
Order:	$338$
Real:	no
Primitive:	no, induced from $\chi_{2197}(389,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8788.ba

$\chi_{8788}(25,\cdot)$ $\chi_{8788}(77,\cdot)$ $\chi_{8788}(129,\cdot)$ $\chi_{8788}(181,\cdot)$ $\chi_{8788}(233,\cdot)$ $\chi_{8788}(285,\cdot)$ $\chi_{8788}(389,\cdot)$ $\chi_{8788}(441,\cdot)$ $\chi_{8788}(493,\cdot)$ $\chi_{8788}(545,\cdot)$ $\chi_{8788}(597,\cdot)$ $\chi_{8788}(649,\cdot)$ $\chi_{8788}(701,\cdot)$ $\chi_{8788}(753,\cdot)$ $\chi_{8788}(805,\cdot)$ $\chi_{8788}(857,\cdot)$ $\chi_{8788}(909,\cdot)$ $\chi_{8788}(961,\cdot)$ $\chi_{8788}(1065,\cdot)$ $\chi_{8788}(1117,\cdot)$ $\chi_{8788}(1169,\cdot)$ $\chi_{8788}(1221,\cdot)$ $\chi_{8788}(1273,\cdot)$ $\chi_{8788}(1325,\cdot)$ $\chi_{8788}(1377,\cdot)$ $\chi_{8788}(1429,\cdot)$ $\chi_{8788}(1481,\cdot)$ $\chi_{8788}(1533,\cdot)$ $\chi_{8788}(1585,\cdot)$ $\chi_{8788}(1637,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{169})$
Fixed field:	Number field defined by a degree 338 polynomial (not computed)

Values on generators

$(4395,6593)$ → $(1,e\left(\frac{305}{338}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 8788 }(389, a)$	$1$	$1$	$e\left(\frac{21}{169}\right)$	$e\left(\frac{327}{338}\right)$	$e\left(\frac{83}{338}\right)$	$e\left(\frac{42}{169}\right)$	$e\left(\frac{163}{338}\right)$	$e\left(\frac{31}{338}\right)$	$e\left(\frac{9}{169}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{125}{338}\right)$	$e\left(\frac{11}{13}\right)$