Dirichlet character \(\chi_{2349}(1195,\cdot)\)

• Label: 2349.1195
• Modulus: $2349$
• Conductor: $2349$
• Order: $378$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2349\)
Conductor:	\(2349\)
Order:	\(378\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2349.bs

\(\chi_{2349}(4,\cdot)\) \(\chi_{2349}(13,\cdot)\) \(\chi_{2349}(22,\cdot)\) \(\chi_{2349}(34,\cdot)\) \(\chi_{2349}(67,\cdot)\) \(\chi_{2349}(121,\cdot)\) \(\chi_{2349}(151,\cdot)\) \(\chi_{2349}(178,\cdot)\) \(\chi_{2349}(187,\cdot)\) \(\chi_{2349}(196,\cdot)\) \(\chi_{2349}(238,\cdot)\) \(\chi_{2349}(241,\cdot)\) \(\chi_{2349}(265,\cdot)\) \(\chi_{2349}(274,\cdot)\) \(\chi_{2349}(283,\cdot)\) \(\chi_{2349}(295,\cdot)\) \(\chi_{2349}(328,\cdot)\) \(\chi_{2349}(382,\cdot)\) \(\chi_{2349}(412,\cdot)\) \(\chi_{2349}(439,\cdot)\) \(\chi_{2349}(448,\cdot)\) \(\chi_{2349}(457,\cdot)\) \(\chi_{2349}(499,\cdot)\) \(\chi_{2349}(502,\cdot)\) \(\chi_{2349}(526,\cdot)\) \(\chi_{2349}(535,\cdot)\) \(\chi_{2349}(544,\cdot)\) \(\chi_{2349}(556,\cdot)\) \(\chi_{2349}(589,\cdot)\) \(\chi_{2349}(643,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{189})$
Fixed field:	Number field defined by a degree 378 polynomial (not computed)

Values on generators

\((407,1945)\) → \((e\left(\frac{26}{27}\right),e\left(\frac{3}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2349 }(1195, a) \)	\(1\)	\(1\)	\(e\left(\frac{67}{378}\right)\)	\(e\left(\frac{67}{189}\right)\)	\(e\left(\frac{163}{189}\right)\)	\(e\left(\frac{185}{189}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{106}{189}\right)\)	\(e\left(\frac{59}{378}\right)\)	\(e\left(\frac{134}{189}\right)\)