Dirichlet character χ5400(1003,⋅)\chi_{5400}(1003,\cdot)

• Label: 5400.1003
• Modulus: $5400$
• Conductor: $5400$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5400$
Conductor:	$5400$
Order:	$180$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5400.fg

$\chi_{5400}(67,\cdot)$ $\chi_{5400}(187,\cdot)$ $\chi_{5400}(283,\cdot)$ $\chi_{5400}(403,\cdot)$ $\chi_{5400}(427,\cdot)$ $\chi_{5400}(547,\cdot)$ $\chi_{5400}(763,\cdot)$ $\chi_{5400}(787,\cdot)$ $\chi_{5400}(1003,\cdot)$ $\chi_{5400}(1123,\cdot)$ $\chi_{5400}(1147,\cdot)$ $\chi_{5400}(1267,\cdot)$ $\chi_{5400}(1363,\cdot)$ $\chi_{5400}(1483,\cdot)$ $\chi_{5400}(1627,\cdot)$ $\chi_{5400}(1723,\cdot)$ $\chi_{5400}(1867,\cdot)$ $\chi_{5400}(1987,\cdot)$ $\chi_{5400}(2083,\cdot)$ $\chi_{5400}(2203,\cdot)$ $\chi_{5400}(2227,\cdot)$ $\chi_{5400}(2347,\cdot)$ $\chi_{5400}(2563,\cdot)$ $\chi_{5400}(2587,\cdot)$ $\chi_{5400}(2803,\cdot)$ $\chi_{5400}(2923,\cdot)$ $\chi_{5400}(2947,\cdot)$ $\chi_{5400}(3067,\cdot)$ $\chi_{5400}(3163,\cdot)$ $\chi_{5400}(3283,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

$(1351,2701,1001,2377)$ → $(-1,-1,e\left(\frac{1}{9}\right),e\left(\frac{7}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 5400 }(1003, a)$	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{45}\right)$