Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 3997.ci
\(\chi_{3997}(2,\cdot)\) \(\chi_{3997}(32,\cdot)\) \(\chi_{3997}(128,\cdot)\) \(\chi_{3997}(135,\cdot)\) \(\chi_{3997}(198,\cdot)\) \(\chi_{3997}(555,\cdot)\) \(\chi_{3997}(646,\cdot)\) \(\chi_{3997}(746,\cdot)\) \(\chi_{3997}(814,\cdot)\) \(\chi_{3997}(872,\cdot)\) \(\chi_{3997}(886,\cdot)\) \(\chi_{3997}(1138,\cdot)\) \(\chi_{3997}(1374,\cdot)\) \(\chi_{3997}(1570,\cdot)\) \(\chi_{3997}(1866,\cdot)\) \(\chi_{3997}(1908,\cdot)\) \(\chi_{3997}(1999,\cdot)\) \(\chi_{3997}(2048,\cdot)\) \(\chi_{3997}(2053,\cdot)\) \(\chi_{3997}(2160,\cdot)\) \(\chi_{3997}(2202,\cdot)\) \(\chi_{3997}(2342,\cdot)\) \(\chi_{3997}(2391,\cdot)\) \(\chi_{3997}(2902,\cdot)\) \(\chi_{3997}(2984,\cdot)\) \(\chi_{3997}(3117,\cdot)\) \(\chi_{3997}(3168,\cdot)\) \(\chi_{3997}(3397,\cdot)\) \(\chi_{3997}(3467,\cdot)\) \(\chi_{3997}(3488,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{109}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) |