Dirichlet character χ4002(3403,⋅)\chi_{4002}(3403,\cdot)

• Label: 4002.3403
• Modulus: $4002$
• Conductor: $667$
• Order: $28$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4002$
Conductor:	$667$
Order:	$28$
Real:	no
Primitive:	no, induced from $\chi_{667}(68,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4002.bd

$\chi_{4002}(229,\cdot)$ $\chi_{4002}(367,\cdot)$ $\chi_{4002}(781,\cdot)$ $\chi_{4002}(1471,\cdot)$ $\chi_{4002}(1609,\cdot)$ $\chi_{4002}(2161,\cdot)$ $\chi_{4002}(2299,\cdot)$ $\chi_{4002}(2989,\cdot)$ $\chi_{4002}(3403,\cdot)$ $\chi_{4002}(3541,\cdot)$ $\chi_{4002}(3817,\cdot)$ $\chi_{4002}(3955,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{28})$
Fixed field:	28.28.35394489068231220324814698212289719250778220848093751207381.1

Values on generators

$(2669,3133,553)$ → $(1,-1,e\left(\frac{23}{28}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$31$	$35$	$37$
$\chi_{ 4002 }(3403, a)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$-i$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{27}{28}\right)$