Basic properties
Modulus: | \(3997\) | |
Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ct
\(\chi_{3997}(17,\cdot)\) \(\chi_{3997}(19,\cdot)\) \(\chi_{3997}(101,\cdot)\) \(\chi_{3997}(234,\cdot)\) \(\chi_{3997}(276,\cdot)\) \(\chi_{3997}(278,\cdot)\) \(\chi_{3997}(348,\cdot)\) \(\chi_{3997}(369,\cdot)\) \(\chi_{3997}(381,\cdot)\) \(\chi_{3997}(402,\cdot)\) \(\chi_{3997}(416,\cdot)\) \(\chi_{3997}(430,\cdot)\) \(\chi_{3997}(474,\cdot)\) \(\chi_{3997}(488,\cdot)\) \(\chi_{3997}(514,\cdot)\) \(\chi_{3997}(537,\cdot)\) \(\chi_{3997}(558,\cdot)\) \(\chi_{3997}(647,\cdot)\) \(\chi_{3997}(684,\cdot)\) \(\chi_{3997}(822,\cdot)\) \(\chi_{3997}(878,\cdot)\) \(\chi_{3997}(915,\cdot)\) \(\chi_{3997}(920,\cdot)\) \(\chi_{3997}(957,\cdot)\) \(\chi_{3997}(962,\cdot)\) \(\chi_{3997}(964,\cdot)\) \(\chi_{3997}(983,\cdot)\) \(\chi_{3997}(985,\cdot)\) \(\chi_{3997}(1046,\cdot)\) \(\chi_{3997}(1062,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{413}{570}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 3997 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{254}{285}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{341}{570}\right)\) | \(e\left(\frac{21}{190}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{223}{285}\right)\) | \(e\left(\frac{233}{285}\right)\) | \(e\left(\frac{242}{285}\right)\) | \(e\left(\frac{94}{285}\right)\) |