Dirichlet character \(\chi_{5184}(709,\cdot)\)

• Label: 5184.709
• Modulus: $5184$
• Conductor: $5184$
• Order: $432$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5184\)
Conductor:	\(5184\)
Order:	\(432\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5184.cy

\(\chi_{5184}(13,\cdot)\) \(\chi_{5184}(61,\cdot)\) \(\chi_{5184}(85,\cdot)\) \(\chi_{5184}(133,\cdot)\) \(\chi_{5184}(157,\cdot)\) \(\chi_{5184}(205,\cdot)\) \(\chi_{5184}(229,\cdot)\) \(\chi_{5184}(277,\cdot)\) \(\chi_{5184}(301,\cdot)\) \(\chi_{5184}(349,\cdot)\) \(\chi_{5184}(373,\cdot)\) \(\chi_{5184}(421,\cdot)\) \(\chi_{5184}(445,\cdot)\) \(\chi_{5184}(493,\cdot)\) \(\chi_{5184}(517,\cdot)\) \(\chi_{5184}(565,\cdot)\) \(\chi_{5184}(589,\cdot)\) \(\chi_{5184}(637,\cdot)\) \(\chi_{5184}(661,\cdot)\) \(\chi_{5184}(709,\cdot)\) \(\chi_{5184}(733,\cdot)\) \(\chi_{5184}(781,\cdot)\) \(\chi_{5184}(805,\cdot)\) \(\chi_{5184}(853,\cdot)\) \(\chi_{5184}(877,\cdot)\) \(\chi_{5184}(925,\cdot)\) \(\chi_{5184}(949,\cdot)\) \(\chi_{5184}(997,\cdot)\) \(\chi_{5184}(1021,\cdot)\) \(\chi_{5184}(1069,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{432})$
Fixed field:	Number field defined by a degree 432 polynomial (not computed)

Values on generators

\((2431,325,1217)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{26}{27}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\( \chi_{ 5184 }(709, a) \)	\(1\)	\(1\)	\(e\left(\frac{91}{432}\right)\)	\(e\left(\frac{7}{216}\right)\)	\(e\left(\frac{359}{432}\right)\)	\(e\left(\frac{277}{432}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{137}{432}\right)\)	\(e\left(\frac{41}{54}\right)\)