Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{571}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.cv
\(\chi_{3997}(113,\cdot)\) \(\chi_{3997}(183,\cdot)\) \(\chi_{3997}(197,\cdot)\) \(\chi_{3997}(239,\cdot)\) \(\chi_{3997}(246,\cdot)\) \(\chi_{3997}(344,\cdot)\) \(\chi_{3997}(358,\cdot)\) \(\chi_{3997}(372,\cdot)\) \(\chi_{3997}(386,\cdot)\) \(\chi_{3997}(393,\cdot)\) \(\chi_{3997}(414,\cdot)\) \(\chi_{3997}(435,\cdot)\) \(\chi_{3997}(456,\cdot)\) \(\chi_{3997}(491,\cdot)\) \(\chi_{3997}(505,\cdot)\) \(\chi_{3997}(519,\cdot)\) \(\chi_{3997}(526,\cdot)\) \(\chi_{3997}(547,\cdot)\) \(\chi_{3997}(589,\cdot)\) \(\chi_{3997}(610,\cdot)\) \(\chi_{3997}(617,\cdot)\) \(\chi_{3997}(624,\cdot)\) \(\chi_{3997}(631,\cdot)\) \(\chi_{3997}(638,\cdot)\) \(\chi_{3997}(645,\cdot)\) \(\chi_{3997}(659,\cdot)\) \(\chi_{3997}(673,\cdot)\) \(\chi_{3997}(701,\cdot)\) \(\chi_{3997}(708,\cdot)\) \(\chi_{3997}(722,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((1,e\left(\frac{1}{570}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(1716, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{1}{570}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{211}{285}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{1}{285}\right)\) | \(e\left(\frac{397}{570}\right)\) | \(e\left(\frac{134}{285}\right)\) | \(e\left(\frac{521}{570}\right)\) |