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 \(\chi_{2167}(239,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.bg
\(\chi_{4334}(29,\cdot)\) \(\chi_{4334}(51,\cdot)\) \(\chi_{4334}(61,\cdot)\) \(\chi_{4334}(63,\cdot)\) \(\chi_{4334}(85,\cdot)\) \(\chi_{4334}(101,\cdot)\) \(\chi_{4334}(105,\cdot)\) \(\chi_{4334}(171,\cdot)\) \(\chi_{4334}(193,\cdot)\) \(\chi_{4334}(237,\cdot)\) \(\chi_{4334}(239,\cdot)\) \(\chi_{4334}(347,\cdot)\) \(\chi_{4334}(369,\cdot)\) \(\chi_{4334}(387,\cdot)\) \(\chi_{4334}(431,\cdot)\) \(\chi_{4334}(447,\cdot)\) \(\chi_{4334}(453,\cdot)\) \(\chi_{4334}(457,\cdot)\) \(\chi_{4334}(475,\cdot)\) \(\chi_{4334}(479,\cdot)\) \(\chi_{4334}(569,\cdot)\) \(\chi_{4334}(607,\cdot)\) \(\chi_{4334}(633,\cdot)\) \(\chi_{4334}(645,\cdot)\) \(\chi_{4334}(651,\cdot)\) \(\chi_{4334}(667,\cdot)\) \(\chi_{4334}(679,\cdot)\) \(\chi_{4334}(723,\cdot)\) \(\chi_{4334}(733,\cdot)\) \(\chi_{4334}(745,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{245})$ |
| Fixed field: | Number field defined by a degree 490 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{33}{49}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(239, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{245}\right)\) | \(e\left(\frac{34}{245}\right)\) | \(e\left(\frac{209}{490}\right)\) | \(e\left(\frac{146}{245}\right)\) | \(e\left(\frac{67}{490}\right)\) | \(e\left(\frac{107}{245}\right)\) | \(e\left(\frac{383}{490}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{71}{98}\right)\) | \(e\left(\frac{40}{49}\right)\) |