Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | 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 3997.bs
\(\chi_{3997}(4,\cdot)\) \(\chi_{3997}(16,\cdot)\) \(\chi_{3997}(256,\cdot)\) \(\chi_{3997}(270,\cdot)\) \(\chi_{3997}(373,\cdot)\) \(\chi_{3997}(396,\cdot)\) \(\chi_{3997}(436,\cdot)\) \(\chi_{3997}(443,\cdot)\) \(\chi_{3997}(569,\cdot)\) \(\chi_{3997}(933,\cdot)\) \(\chi_{3997}(954,\cdot)\) \(\chi_{3997}(1024,\cdot)\) \(\chi_{3997}(1080,\cdot)\) \(\chi_{3997}(1101,\cdot)\) \(\chi_{3997}(1110,\cdot)\) \(\chi_{3997}(1171,\cdot)\) \(\chi_{3997}(1292,\cdot)\) \(\chi_{3997}(1362,\cdot)\) \(\chi_{3997}(1451,\cdot)\) \(\chi_{3997}(1584,\cdot)\) \(\chi_{3997}(1628,\cdot)\) \(\chi_{3997}(1971,\cdot)\) \(\chi_{3997}(2237,\cdot)\) \(\chi_{3997}(2515,\cdot)\) \(\chi_{3997}(2748,\cdot)\) \(\chi_{3997}(2797,\cdot)\) \(\chi_{3997}(2937,\cdot)\) \(\chi_{3997}(2979,\cdot)\) \(\chi_{3997}(2998,\cdot)\) \(\chi_{3997}(3091,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((2285,1716)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{52}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) |