Basic properties
| Modulus: | \(1051\) | |
| Conductor: | \(1051\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1050\) | 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 1051.x
\(\chi_{1051}(7,\cdot)\) \(\chi_{1051}(10,\cdot)\) \(\chi_{1051}(12,\cdot)\) \(\chi_{1051}(13,\cdot)\) \(\chi_{1051}(17,\cdot)\) \(\chi_{1051}(18,\cdot)\) \(\chi_{1051}(22,\cdot)\) \(\chi_{1051}(23,\cdot)\) \(\chi_{1051}(31,\cdot)\) \(\chi_{1051}(33,\cdot)\) \(\chi_{1051}(37,\cdot)\) \(\chi_{1051}(40,\cdot)\) \(\chi_{1051}(41,\cdot)\) \(\chi_{1051}(42,\cdot)\) \(\chi_{1051}(47,\cdot)\) \(\chi_{1051}(48,\cdot)\) \(\chi_{1051}(52,\cdot)\) \(\chi_{1051}(58,\cdot)\) \(\chi_{1051}(59,\cdot)\) \(\chi_{1051}(68,\cdot)\) \(\chi_{1051}(71,\cdot)\) \(\chi_{1051}(72,\cdot)\) \(\chi_{1051}(73,\cdot)\) \(\chi_{1051}(76,\cdot)\) \(\chi_{1051}(77,\cdot)\) \(\chi_{1051}(90,\cdot)\) \(\chi_{1051}(92,\cdot)\) \(\chi_{1051}(98,\cdot)\) \(\chi_{1051}(101,\cdot)\) \(\chi_{1051}(109,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{525})$ |
| Fixed field: | Number field defined by a degree 1050 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{1}{1050}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1051 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{350}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{9}{175}\right)\) | \(e\left(\frac{58}{525}\right)\) | \(e\left(\frac{146}{525}\right)\) | \(e\left(\frac{1}{1050}\right)\) | \(e\left(\frac{27}{350}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{143}{1050}\right)\) | \(e\left(\frac{383}{525}\right)\) |