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.bf
\(\chi_{847}(2,\cdot)\) \(\chi_{847}(18,\cdot)\) \(\chi_{847}(30,\cdot)\) \(\chi_{847}(39,\cdot)\) \(\chi_{847}(46,\cdot)\) \(\chi_{847}(51,\cdot)\) \(\chi_{847}(72,\cdot)\) \(\chi_{847}(74,\cdot)\) \(\chi_{847}(79,\cdot)\) \(\chi_{847}(95,\cdot)\) \(\chi_{847}(107,\cdot)\) \(\chi_{847}(116,\cdot)\) \(\chi_{847}(123,\cdot)\) \(\chi_{847}(128,\cdot)\) \(\chi_{847}(149,\cdot)\) \(\chi_{847}(151,\cdot)\) \(\chi_{847}(156,\cdot)\) \(\chi_{847}(172,\cdot)\) \(\chi_{847}(184,\cdot)\) \(\chi_{847}(193,\cdot)\) \(\chi_{847}(200,\cdot)\) \(\chi_{847}(205,\cdot)\) \(\chi_{847}(226,\cdot)\) \(\chi_{847}(228,\cdot)\) \(\chi_{847}(249,\cdot)\) \(\chi_{847}(261,\cdot)\) \(\chi_{847}(270,\cdot)\) \(\chi_{847}(277,\cdot)\) \(\chi_{847}(303,\cdot)\) \(\chi_{847}(305,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((122,365)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{79}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{59}{110}\right)\) |