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.cg
\(\chi_{3997}(31,\cdot)\) \(\chi_{3997}(59,\cdot)\) \(\chi_{3997}(94,\cdot)\) \(\chi_{3997}(131,\cdot)\) \(\chi_{3997}(271,\cdot)\) \(\chi_{3997}(306,\cdot)\) \(\chi_{3997}(353,\cdot)\) \(\chi_{3997}(390,\cdot)\) \(\chi_{3997}(563,\cdot)\) \(\chi_{3997}(626,\cdot)\) \(\chi_{3997}(635,\cdot)\) \(\chi_{3997}(670,\cdot)\) \(\chi_{3997}(894,\cdot)\) \(\chi_{3997}(978,\cdot)\) \(\chi_{3997}(1258,\cdot)\) \(\chi_{3997}(1312,\cdot)\) \(\chi_{3997}(1356,\cdot)\) \(\chi_{3997}(1844,\cdot)\) \(\chi_{3997}(1984,\cdot)\) \(\chi_{3997}(2019,\cdot)\) \(\chi_{3997}(2063,\cdot)\) \(\chi_{3997}(2103,\cdot)\) \(\chi_{3997}(2315,\cdot)\) \(\chi_{3997}(2343,\cdot)\) \(\chi_{3997}(2348,\cdot)\) \(\chi_{3997}(2378,\cdot)\) \(\chi_{3997}(2383,\cdot)\) \(\chi_{3997}(2607,\cdot)\) \(\chi_{3997}(2637,\cdot)\) \(\chi_{3997}(2691,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) |