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.ce
\(\chi_{3997}(258,\cdot)\) \(\chi_{3997}(328,\cdot)\) \(\chi_{3997}(496,\cdot)\) \(\chi_{3997}(524,\cdot)\) \(\chi_{3997}(587,\cdot)\) \(\chi_{3997}(944,\cdot)\) \(\chi_{3997}(1007,\cdot)\) \(\chi_{3997}(1014,\cdot)\) \(\chi_{3997}(1035,\cdot)\) \(\chi_{3997}(1084,\cdot)\) \(\chi_{3997}(1140,\cdot)\) \(\chi_{3997}(1224,\cdot)\) \(\chi_{3997}(1266,\cdot)\) \(\chi_{3997}(1378,\cdot)\) \(\chi_{3997}(1427,\cdot)\) \(\chi_{3997}(1504,\cdot)\) \(\chi_{3997}(1518,\cdot)\) \(\chi_{3997}(1525,\cdot)\) \(\chi_{3997}(1560,\cdot)\) \(\chi_{3997}(1595,\cdot)\) \(\chi_{3997}(1651,\cdot)\) \(\chi_{3997}(1672,\cdot)\) \(\chi_{3997}(1742,\cdot)\) \(\chi_{3997}(2022,\cdot)\) \(\chi_{3997}(2155,\cdot)\) \(\chi_{3997}(2288,\cdot)\) \(\chi_{3997}(2540,\cdot)\) \(\chi_{3997}(2554,\cdot)\) \(\chi_{3997}(2680,\cdot)\) \(\chi_{3997}(3086,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((-1,e\left(\frac{43}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(258, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) |