Dirichlet character χ4675(1417,⋅)\chi_{4675}(1417,\cdot)

• Label: 4675.1417
• Modulus: $4675$
• Conductor: $4675$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4675$
Conductor:	$4675$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4675.jh

$\chi_{4675}(48,\cdot)$ $\chi_{4675}(317,\cdot)$ $\chi_{4675}(388,\cdot)$ $\chi_{4675}(487,\cdot)$ $\chi_{4675}(598,\cdot)$ $\chi_{4675}(658,\cdot)$ $\chi_{4675}(753,\cdot)$ $\chi_{4675}(938,\cdot)$ $\chi_{4675}(1027,\cdot)$ $\chi_{4675}(1302,\cdot)$ $\chi_{4675}(1417,\cdot)$ $\chi_{4675}(1423,\cdot)$ $\chi_{4675}(1578,\cdot)$ $\chi_{4675}(1587,\cdot)$ $\chi_{4675}(1622,\cdot)$ $\chi_{4675}(1763,\cdot)$ $\chi_{4675}(1897,\cdot)$ $\chi_{4675}(2128,\cdot)$ $\chi_{4675}(2952,\cdot)$ $\chi_{4675}(2953,\cdot)$ $\chi_{4675}(3067,\cdot)$ $\chi_{4675}(3133,\cdot)$ $\chi_{4675}(3237,\cdot)$ $\chi_{4675}(3342,\cdot)$ $\chi_{4675}(3512,\cdot)$ $\chi_{4675}(3547,\cdot)$ $\chi_{4675}(3898,\cdot)$ $\chi_{4675}(3958,\cdot)$ $\chi_{4675}(4052,\cdot)$ $\chi_{4675}(4238,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

$(4302,3401,3301)$ → $(e\left(\frac{13}{20}\right),e\left(\frac{3}{5}\right),e\left(\frac{15}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{ 4675 }(1417, a)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{80}\right)$	$-i$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{80}\right)$