Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | 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.cu
\(\chi_{3997}(39,\cdot)\) \(\chi_{3997}(46,\cdot)\) \(\chi_{3997}(67,\cdot)\) \(\chi_{3997}(79,\cdot)\) \(\chi_{3997}(93,\cdot)\) \(\chi_{3997}(102,\cdot)\) \(\chi_{3997}(114,\cdot)\) \(\chi_{3997}(130,\cdot)\) \(\chi_{3997}(137,\cdot)\) \(\chi_{3997}(177,\cdot)\) \(\chi_{3997}(205,\cdot)\) \(\chi_{3997}(249,\cdot)\) \(\chi_{3997}(282,\cdot)\) \(\chi_{3997}(284,\cdot)\) \(\chi_{3997}(291,\cdot)\) \(\chi_{3997}(298,\cdot)\) \(\chi_{3997}(310,\cdot)\) \(\chi_{3997}(326,\cdot)\) \(\chi_{3997}(338,\cdot)\) \(\chi_{3997}(380,\cdot)\) \(\chi_{3997}(452,\cdot)\) \(\chi_{3997}(487,\cdot)\) \(\chi_{3997}(557,\cdot)\) \(\chi_{3997}(590,\cdot)\) \(\chi_{3997}(606,\cdot)\) \(\chi_{3997}(634,\cdot)\) \(\chi_{3997}(683,\cdot)\) \(\chi_{3997}(774,\cdot)\) \(\chi_{3997}(781,\cdot)\) \(\chi_{3997}(830,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{353}{570}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{163}{570}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{193}{285}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{163}{285}\right)\) | \(e\left(\frac{301}{570}\right)\) | \(e\left(\frac{182}{285}\right)\) | \(e\left(\frac{563}{570}\right)\) |