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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.cz
\(\chi_{3997}(13,\cdot)\) \(\chi_{3997}(34,\cdot)\) \(\chi_{3997}(83,\cdot)\) \(\chi_{3997}(97,\cdot)\) \(\chi_{3997}(139,\cdot)\) \(\chi_{3997}(174,\cdot)\) \(\chi_{3997}(202,\cdot)\) \(\chi_{3997}(223,\cdot)\) \(\chi_{3997}(237,\cdot)\) \(\chi_{3997}(244,\cdot)\) \(\chi_{3997}(279,\cdot)\) \(\chi_{3997}(293,\cdot)\) \(\chi_{3997}(321,\cdot)\) \(\chi_{3997}(342,\cdot)\) \(\chi_{3997}(482,\cdot)\) \(\chi_{3997}(531,\cdot)\) \(\chi_{3997}(538,\cdot)\) \(\chi_{3997}(552,\cdot)\) \(\chi_{3997}(559,\cdot)\) \(\chi_{3997}(580,\cdot)\) \(\chi_{3997}(601,\cdot)\) \(\chi_{3997}(608,\cdot)\) \(\chi_{3997}(615,\cdot)\) \(\chi_{3997}(671,\cdot)\) \(\chi_{3997}(692,\cdot)\) \(\chi_{3997}(762,\cdot)\) \(\chi_{3997}(790,\cdot)\) \(\chi_{3997}(804,\cdot)\) \(\chi_{3997}(832,\cdot)\) \(\chi_{3997}(846,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((-1,e\left(\frac{217}{285}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 3997 }(342, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{149}{570}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{463}{570}\right)\) | \(e\left(\frac{43}{190}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{149}{285}\right)\) | \(e\left(\frac{443}{570}\right)\) | \(e\left(\frac{16}{285}\right)\) | \(e\left(\frac{109}{570}\right)\) |