Basic properties
| Modulus: | \(36864\) | |
| Conductor: | \(36864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3072\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
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
\((8191,20485,4097)\) → \((1,e\left(\frac{287}{1024}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 36864 }(589, a) \) | \(1\) | \(1\) | \(e\left(\frac{2909}{3072}\right)\) | \(e\left(\frac{689}{1536}\right)\) | \(e\left(\frac{97}{3072}\right)\) | \(e\left(\frac{2771}{3072}\right)\) | \(e\left(\frac{121}{256}\right)\) | \(e\left(\frac{585}{1024}\right)\) | \(e\left(\frac{715}{1536}\right)\) | \(e\left(\frac{1373}{1536}\right)\) | \(e\left(\frac{175}{3072}\right)\) | \(e\left(\frac{205}{384}\right)\) |