Dirichlet character \(\chi_{373527}(12506,\cdot)\)

• Label: 373527.12506
• Modulus: $373527$
• Conductor: $373527$
• Order: $3234$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(373527\)
Conductor:	\(373527\)
Order:	\(3234\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 373527.qd

\(\chi_{373527}(32,\cdot)\) \(\chi_{373527}(65,\cdot)\) \(\chi_{373527}(758,\cdot)\) \(\chi_{373527}(1418,\cdot)\) \(\chi_{373527}(2111,\cdot)\) \(\chi_{373527}(2144,\cdot)\) \(\chi_{373527}(2804,\cdot)\) \(\chi_{373527}(2837,\cdot)\) \(\chi_{373527}(3530,\cdot)\) \(\chi_{373527}(4190,\cdot)\) \(\chi_{373527}(4223,\cdot)\) \(\chi_{373527}(4883,\cdot)\) \(\chi_{373527}(4916,\cdot)\) \(\chi_{373527}(5576,\cdot)\) \(\chi_{373527}(5609,\cdot)\) \(\chi_{373527}(6269,\cdot)\) \(\chi_{373527}(6962,\cdot)\) \(\chi_{373527}(6995,\cdot)\) \(\chi_{373527}(7655,\cdot)\) \(\chi_{373527}(7688,\cdot)\) \(\chi_{373527}(8381,\cdot)\) \(\chi_{373527}(9041,\cdot)\) \(\chi_{373527}(9734,\cdot)\) \(\chi_{373527}(9767,\cdot)\) \(\chi_{373527}(10427,\cdot)\) \(\chi_{373527}(10460,\cdot)\) \(\chi_{373527}(11120,\cdot)\) \(\chi_{373527}(11813,\cdot)\) \(\chi_{373527}(11846,\cdot)\) \(\chi_{373527}(12506,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{1617})$
Fixed field:	Number field defined by a degree 3234 polynomial (not computed)

Values on generators

\((290522,286408,126568)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{125}{147}\right),e\left(\frac{5}{22}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 373527 }(12506, a) \)	\(1\)	\(1\)	\(e\left(\frac{43}{1617}\right)\)	\(e\left(\frac{86}{1617}\right)\)	\(e\left(\frac{695}{1078}\right)\)	\(e\left(\frac{43}{539}\right)\)	\(e\left(\frac{2171}{3234}\right)\)	\(e\left(\frac{3131}{3234}\right)\)	\(e\left(\frac{172}{1617}\right)\)	\(e\left(\frac{1447}{1617}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2257}{3234}\right)\)