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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.cr
\(\chi_{3997}(26,\cdot)\) \(\chi_{3997}(68,\cdot)\) \(\chi_{3997}(87,\cdot)\) \(\chi_{3997}(122,\cdot)\) \(\chi_{3997}(166,\cdot)\) \(\chi_{3997}(171,\cdot)\) \(\chi_{3997}(187,\cdot)\) \(\chi_{3997}(194,\cdot)\) \(\chi_{3997}(241,\cdot)\) \(\chi_{3997}(269,\cdot)\) \(\chi_{3997}(290,\cdot)\) \(\chi_{3997}(304,\cdot)\) \(\chi_{3997}(346,\cdot)\) \(\chi_{3997}(355,\cdot)\) \(\chi_{3997}(395,\cdot)\) \(\chi_{3997}(423,\cdot)\) \(\chi_{3997}(425,\cdot)\) \(\chi_{3997}(446,\cdot)\) \(\chi_{3997}(451,\cdot)\) \(\chi_{3997}(535,\cdot)\) \(\chi_{3997}(551,\cdot)\) \(\chi_{3997}(565,\cdot)\) \(\chi_{3997}(586,\cdot)\) \(\chi_{3997}(593,\cdot)\) \(\chi_{3997}(598,\cdot)\) \(\chi_{3997}(619,\cdot)\) \(\chi_{3997}(621,\cdot)\) \(\chi_{3997}(682,\cdot)\) \(\chi_{3997}(703,\cdot)\) \(\chi_{3997}(731,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{109}{190}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{116}{285}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{149}{570}\right)\) | \(e\left(\frac{139}{190}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{232}{285}\right)\) | \(e\left(\frac{167}{285}\right)\) | \(e\left(\frac{23}{285}\right)\) | \(e\left(\frac{16}{285}\right)\) |