Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(285\) | 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.cm
\(\chi_{3997}(9,\cdot)\) \(\chi_{3997}(11,\cdot)\) \(\chi_{3997}(25,\cdot)\) \(\chi_{3997}(30,\cdot)\) \(\chi_{3997}(37,\cdot)\) \(\chi_{3997}(44,\cdot)\) \(\chi_{3997}(81,\cdot)\) \(\chi_{3997}(100,\cdot)\) \(\chi_{3997}(121,\cdot)\) \(\chi_{3997}(144,\cdot)\) \(\chi_{3997}(219,\cdot)\) \(\chi_{3997}(275,\cdot)\) \(\chi_{3997}(324,\cdot)\) \(\chi_{3997}(333,\cdot)\) \(\chi_{3997}(359,\cdot)\) \(\chi_{3997}(403,\cdot)\) \(\chi_{3997}(424,\cdot)\) \(\chi_{3997}(480,\cdot)\) \(\chi_{3997}(494,\cdot)\) \(\chi_{3997}(499,\cdot)\) \(\chi_{3997}(543,\cdot)\) \(\chi_{3997}(576,\cdot)\) \(\chi_{3997}(592,\cdot)\) \(\chi_{3997}(625,\cdot)\) \(\chi_{3997}(641,\cdot)\) \(\chi_{3997}(667,\cdot)\) \(\chi_{3997}(697,\cdot)\) \(\chi_{3997}(704,\cdot)\) \(\chi_{3997}(730,\cdot)\) \(\chi_{3997}(751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 285 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{166}{285}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{54}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) |