Basic properties
| Modulus: | \(2167\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(490\) | 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 2167.bf
\(\chi_{2167}(24,\cdot)\) \(\chi_{2167}(28,\cdot)\) \(\chi_{2167}(29,\cdot)\) \(\chi_{2167}(40,\cdot)\) \(\chi_{2167}(51,\cdot)\) \(\chi_{2167}(61,\cdot)\) \(\chi_{2167}(63,\cdot)\) \(\chi_{2167}(85,\cdot)\) \(\chi_{2167}(90,\cdot)\) \(\chi_{2167}(101,\cdot)\) \(\chi_{2167}(105,\cdot)\) \(\chi_{2167}(150,\cdot)\) \(\chi_{2167}(156,\cdot)\) \(\chi_{2167}(171,\cdot)\) \(\chi_{2167}(172,\cdot)\) \(\chi_{2167}(182,\cdot)\) \(\chi_{2167}(193,\cdot)\) \(\chi_{2167}(226,\cdot)\) \(\chi_{2167}(237,\cdot)\) \(\chi_{2167}(239,\cdot)\) \(\chi_{2167}(248,\cdot)\) \(\chi_{2167}(250,\cdot)\) \(\chi_{2167}(260,\cdot)\) \(\chi_{2167}(282,\cdot)\) \(\chi_{2167}(332,\cdot)\) \(\chi_{2167}(347,\cdot)\) \(\chi_{2167}(369,\cdot)\) \(\chi_{2167}(387,\cdot)\) \(\chi_{2167}(431,\cdot)\) \(\chi_{2167}(436,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{245})$ |
| Fixed field: | Number field defined by a degree 490 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{16}{49}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2167 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{111}{490}\right)\) | \(e\left(\frac{74}{245}\right)\) | \(e\left(\frac{111}{245}\right)\) | \(e\left(\frac{162}{245}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{477}{490}\right)\) | \(e\left(\frac{333}{490}\right)\) | \(e\left(\frac{148}{245}\right)\) | \(e\left(\frac{87}{98}\right)\) | \(e\left(\frac{37}{49}\right)\) |