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.db
\(\chi_{3997}(3,\cdot)\) \(\chi_{3997}(10,\cdot)\) \(\chi_{3997}(12,\cdot)\) \(\chi_{3997}(33,\cdot)\) \(\chi_{3997}(40,\cdot)\) \(\chi_{3997}(73,\cdot)\) \(\chi_{3997}(89,\cdot)\) \(\chi_{3997}(108,\cdot)\) \(\chi_{3997}(192,\cdot)\) \(\chi_{3997}(229,\cdot)\) \(\chi_{3997}(250,\cdot)\) \(\chi_{3997}(292,\cdot)\) \(\chi_{3997}(297,\cdot)\) \(\chi_{3997}(311,\cdot)\) \(\chi_{3997}(318,\cdot)\) \(\chi_{3997}(327,\cdot)\) \(\chi_{3997}(334,\cdot)\) \(\chi_{3997}(360,\cdot)\) \(\chi_{3997}(367,\cdot)\) \(\chi_{3997}(397,\cdot)\) \(\chi_{3997}(432,\cdot)\) \(\chi_{3997}(444,\cdot)\) \(\chi_{3997}(479,\cdot)\) \(\chi_{3997}(493,\cdot)\) \(\chi_{3997}(528,\cdot)\) \(\chi_{3997}(675,\cdot)\) \(\chi_{3997}(754,\cdot)\) \(\chi_{3997}(768,\cdot)\) \(\chi_{3997}(801,\cdot)\) \(\chi_{3997}(810,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{521}{570}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{169}{190}\right)\) | \(e\left(\frac{107}{190}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{67}{95}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{36}{95}\right)\) |