Basic properties
| Modulus: | \(4334\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(490\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2167}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.bf
\(\chi_{4334}(7,\cdot)\) \(\chi_{4334}(39,\cdot)\) \(\chi_{4334}(41,\cdot)\) \(\chi_{4334}(107,\cdot)\) \(\chi_{4334}(127,\cdot)\) \(\chi_{4334}(173,\cdot)\) \(\chi_{4334}(259,\cdot)\) \(\chi_{4334}(261,\cdot)\) \(\chi_{4334}(293,\cdot)\) \(\chi_{4334}(343,\cdot)\) \(\chi_{4334}(365,\cdot)\) \(\chi_{4334}(371,\cdot)\) \(\chi_{4334}(403,\cdot)\) \(\chi_{4334}(409,\cdot)\) \(\chi_{4334}(435,\cdot)\) \(\chi_{4334}(437,\cdot)\) \(\chi_{4334}(459,\cdot)\) \(\chi_{4334}(491,\cdot)\) \(\chi_{4334}(501,\cdot)\) \(\chi_{4334}(503,\cdot)\) \(\chi_{4334}(557,\cdot)\) \(\chi_{4334}(563,\cdot)\) \(\chi_{4334}(567,\cdot)\) \(\chi_{4334}(601,\cdot)\) \(\chi_{4334}(613,\cdot)\) \(\chi_{4334}(655,\cdot)\) \(\chi_{4334}(739,\cdot)\) \(\chi_{4334}(765,\cdot)\) \(\chi_{4334}(827,\cdot)\) \(\chi_{4334}(831,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{245})$ |
| Fixed field: | Number field defined by a degree 490 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{73}{98}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{209}{490}\right)\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{321}{490}\right)\) | \(e\left(\frac{209}{245}\right)\) | \(e\left(\frac{79}{245}\right)\) | \(e\left(\frac{128}{245}\right)\) | \(e\left(\frac{181}{245}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{19}{49}\right)\) |