Dirichlet character χ6900(19,⋅)\chi_{6900}(19,\cdot)

• Label: 6900.19
• Modulus: $6900$
• Conductor: $2300$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$6900$
Conductor:	$2300$
Order:	$110$
Real:	no
Primitive:	no, induced from $\chi_{2300}(19,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 6900.dh

$\chi_{6900}(19,\cdot)$ $\chi_{6900}(79,\cdot)$ $\chi_{6900}(319,\cdot)$ $\chi_{6900}(379,\cdot)$ $\chi_{6900}(559,\cdot)$ $\chi_{6900}(619,\cdot)$ $\chi_{6900}(1279,\cdot)$ $\chi_{6900}(1339,\cdot)$ $\chi_{6900}(1459,\cdot)$ $\chi_{6900}(1579,\cdot)$ $\chi_{6900}(1759,\cdot)$ $\chi_{6900}(1939,\cdot)$ $\chi_{6900}(2179,\cdot)$ $\chi_{6900}(2659,\cdot)$ $\chi_{6900}(2719,\cdot)$ $\chi_{6900}(2779,\cdot)$ $\chi_{6900}(2839,\cdot)$ $\chi_{6900}(2959,\cdot)$ $\chi_{6900}(3079,\cdot)$ $\chi_{6900}(3139,\cdot)$ $\chi_{6900}(3319,\cdot)$ $\chi_{6900}(3379,\cdot)$ $\chi_{6900}(3559,\cdot)$ $\chi_{6900}(4039,\cdot)$ $\chi_{6900}(4159,\cdot)$ $\chi_{6900}(4219,\cdot)$ $\chi_{6900}(4339,\cdot)$ $\chi_{6900}(4459,\cdot)$ $\chi_{6900}(4519,\cdot)$ $\chi_{6900}(4759,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

$(3451,4601,277,1201)$ → $(-1,1,e\left(\frac{9}{10}\right),e\left(\frac{15}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 6900 }(19, a)$	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{22}\right)$