Dirichlet character χ43200(21397,⋅)\chi_{43200}(21397,\cdot)

• Label: 43200.21397
• Modulus: $43200$
• Conductor: $43200$
• Order: $720$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$43200$
Conductor:	$43200$
Order:	$720$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 43200.qn

$\chi_{43200}(13,\cdot)$ $\chi_{43200}(277,\cdot)$ $\chi_{43200}(517,\cdot)$ $\chi_{43200}(733,\cdot)$ $\chi_{43200}(997,\cdot)$ $\chi_{43200}(1213,\cdot)$ $\chi_{43200}(1237,\cdot)$ $\chi_{43200}(1453,\cdot)$ $\chi_{43200}(1717,\cdot)$ $\chi_{43200}(1933,\cdot)$ $\chi_{43200}(2173,\cdot)$ $\chi_{43200}(2437,\cdot)$ $\chi_{43200}(2653,\cdot)$ $\chi_{43200}(2677,\cdot)$ $\chi_{43200}(3373,\cdot)$ $\chi_{43200}(3397,\cdot)$ $\chi_{43200}(3613,\cdot)$ $\chi_{43200}(3877,\cdot)$ $\chi_{43200}(4117,\cdot)$ $\chi_{43200}(4333,\cdot)$ $\chi_{43200}(4597,\cdot)$ $\chi_{43200}(4813,\cdot)$ $\chi_{43200}(4837,\cdot)$ $\chi_{43200}(5053,\cdot)$ $\chi_{43200}(5317,\cdot)$ $\chi_{43200}(5533,\cdot)$ $\chi_{43200}(5773,\cdot)$ $\chi_{43200}(6037,\cdot)$ $\chi_{43200}(6253,\cdot)$ $\chi_{43200}(6277,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{720})$
Fixed field:	Number field defined by a degree 720 polynomial (not computed)

Values on generators

$(28351,29701,6401,29377)$ → $(1,e\left(\frac{13}{16}\right),e\left(\frac{4}{9}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 43200 }(21397, a)$	$-1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{317}{720}\right)$	$e\left(\frac{643}{720}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{221}{360}\right)$	$e\left(\frac{59}{720}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{119}{360}\right)$