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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 847.be
\(\chi_{847}(17,\cdot)\) \(\chi_{847}(19,\cdot)\) \(\chi_{847}(24,\cdot)\) \(\chi_{847}(52,\cdot)\) \(\chi_{847}(61,\cdot)\) \(\chi_{847}(68,\cdot)\) \(\chi_{847}(73,\cdot)\) \(\chi_{847}(96,\cdot)\) \(\chi_{847}(101,\cdot)\) \(\chi_{847}(117,\cdot)\) \(\chi_{847}(129,\cdot)\) \(\chi_{847}(138,\cdot)\) \(\chi_{847}(145,\cdot)\) \(\chi_{847}(150,\cdot)\) \(\chi_{847}(171,\cdot)\) \(\chi_{847}(173,\cdot)\) \(\chi_{847}(178,\cdot)\) \(\chi_{847}(194,\cdot)\) \(\chi_{847}(206,\cdot)\) \(\chi_{847}(222,\cdot)\) \(\chi_{847}(227,\cdot)\) \(\chi_{847}(248,\cdot)\) \(\chi_{847}(250,\cdot)\) \(\chi_{847}(255,\cdot)\) \(\chi_{847}(271,\cdot)\) \(\chi_{847}(283,\cdot)\) \(\chi_{847}(292,\cdot)\) \(\chi_{847}(299,\cdot)\) \(\chi_{847}(304,\cdot)\) \(\chi_{847}(325,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((122,365)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{101}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(255, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{13}{55}\right)\) |