Dirichlet character \(\chi_{36864}(1021,\cdot)\)

• Label: 36864.1021
• Modulus: $36864$
• Conductor: $36864$
• Order: $3072$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(36864\)
Conductor:	\(36864\)
Order:	\(3072\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 36864.di

\(\chi_{36864}(13,\cdot)\) \(\chi_{36864}(61,\cdot)\) \(\chi_{36864}(85,\cdot)\) \(\chi_{36864}(133,\cdot)\) \(\chi_{36864}(157,\cdot)\) \(\chi_{36864}(205,\cdot)\) \(\chi_{36864}(229,\cdot)\) \(\chi_{36864}(277,\cdot)\) \(\chi_{36864}(301,\cdot)\) \(\chi_{36864}(349,\cdot)\) \(\chi_{36864}(373,\cdot)\) \(\chi_{36864}(421,\cdot)\) \(\chi_{36864}(445,\cdot)\) \(\chi_{36864}(493,\cdot)\) \(\chi_{36864}(517,\cdot)\) \(\chi_{36864}(565,\cdot)\) \(\chi_{36864}(589,\cdot)\) \(\chi_{36864}(637,\cdot)\) \(\chi_{36864}(661,\cdot)\) \(\chi_{36864}(709,\cdot)\) \(\chi_{36864}(733,\cdot)\) \(\chi_{36864}(781,\cdot)\) \(\chi_{36864}(805,\cdot)\) \(\chi_{36864}(853,\cdot)\) \(\chi_{36864}(877,\cdot)\) \(\chi_{36864}(925,\cdot)\) \(\chi_{36864}(949,\cdot)\) \(\chi_{36864}(997,\cdot)\) \(\chi_{36864}(1021,\cdot)\) \(\chi_{36864}(1069,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{3072})$
Fixed field:	Number field defined by a degree 3072 polynomial (not computed)

Values on generators

\((8191,20485,4097)\) → \((1,e\left(\frac{419}{1024}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\( \chi_{ 36864 }(1021, a) \)	\(1\)	\(1\)	\(e\left(\frac{233}{3072}\right)\)	\(e\left(\frac{749}{1536}\right)\)	\(e\left(\frac{1501}{3072}\right)\)	\(e\left(\frac{2183}{3072}\right)\)	\(e\left(\frac{149}{256}\right)\)	\(e\left(\frac{37}{1024}\right)\)	\(e\left(\frac{1183}{1536}\right)\)	\(e\left(\frac{233}{1536}\right)\)	\(e\left(\frac{2803}{3072}\right)\)	\(e\left(\frac{25}{384}\right)\)