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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.cx
\(\chi_{3997}(38,\cdot)\) \(\chi_{3997}(117,\cdot)\) \(\chi_{3997}(138,\cdot)\) \(\chi_{3997}(201,\cdot)\) \(\chi_{3997}(206,\cdot)\) \(\chi_{3997}(208,\cdot)\) \(\chi_{3997}(215,\cdot)\) \(\chi_{3997}(257,\cdot)\) \(\chi_{3997}(283,\cdot)\) \(\chi_{3997}(409,\cdot)\) \(\chi_{3997}(411,\cdot)\) \(\chi_{3997}(439,\cdot)\) \(\chi_{3997}(460,\cdot)\) \(\chi_{3997}(521,\cdot)\) \(\chi_{3997}(523,\cdot)\) \(\chi_{3997}(544,\cdot)\) \(\chi_{3997}(549,\cdot)\) \(\chi_{3997}(556,\cdot)\) \(\chi_{3997}(577,\cdot)\) \(\chi_{3997}(591,\cdot)\) \(\chi_{3997}(607,\cdot)\) \(\chi_{3997}(691,\cdot)\) \(\chi_{3997}(696,\cdot)\) \(\chi_{3997}(717,\cdot)\) \(\chi_{3997}(719,\cdot)\) \(\chi_{3997}(747,\cdot)\) \(\chi_{3997}(787,\cdot)\) \(\chi_{3997}(796,\cdot)\) \(\chi_{3997}(838,\cdot)\) \(\chi_{3997}(852,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{72}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 3997 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{527}{570}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{379}{570}\right)\) | \(e\left(\frac{59}{190}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{242}{285}\right)\) | \(e\left(\frac{29}{570}\right)\) | \(e\left(\frac{223}{285}\right)\) | \(e\left(\frac{397}{570}\right)\) |