Basic properties
| Modulus: | \(847\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 847.bd
\(\chi_{847}(5,\cdot)\) \(\chi_{847}(26,\cdot)\) \(\chi_{847}(31,\cdot)\) \(\chi_{847}(38,\cdot)\) \(\chi_{847}(47,\cdot)\) \(\chi_{847}(59,\cdot)\) \(\chi_{847}(75,\cdot)\) \(\chi_{847}(80,\cdot)\) \(\chi_{847}(82,\cdot)\) \(\chi_{847}(103,\cdot)\) \(\chi_{847}(108,\cdot)\) \(\chi_{847}(115,\cdot)\) \(\chi_{847}(136,\cdot)\) \(\chi_{847}(152,\cdot)\) \(\chi_{847}(157,\cdot)\) \(\chi_{847}(159,\cdot)\) \(\chi_{847}(180,\cdot)\) \(\chi_{847}(185,\cdot)\) \(\chi_{847}(192,\cdot)\) \(\chi_{847}(201,\cdot)\) \(\chi_{847}(213,\cdot)\) \(\chi_{847}(229,\cdot)\) \(\chi_{847}(234,\cdot)\) \(\chi_{847}(236,\cdot)\) \(\chi_{847}(257,\cdot)\) \(\chi_{847}(262,\cdot)\) \(\chi_{847}(278,\cdot)\) \(\chi_{847}(290,\cdot)\) \(\chi_{847}(306,\cdot)\) \(\chi_{847}(311,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((122,365)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{42}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{69}{110}\right)\) |