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.cq
\(\chi_{3997}(5,\cdot)\) \(\chi_{3997}(24,\cdot)\) \(\chi_{3997}(45,\cdot)\) \(\chi_{3997}(54,\cdot)\) \(\chi_{3997}(66,\cdot)\) \(\chi_{3997}(80,\cdot)\) \(\chi_{3997}(96,\cdot)\) \(\chi_{3997}(157,\cdot)\) \(\chi_{3997}(159,\cdot)\) \(\chi_{3997}(178,\cdot)\) \(\chi_{3997}(180,\cdot)\) \(\chi_{3997}(185,\cdot)\) \(\chi_{3997}(222,\cdot)\) \(\chi_{3997}(227,\cdot)\) \(\chi_{3997}(264,\cdot)\) \(\chi_{3997}(320,\cdot)\) \(\chi_{3997}(458,\cdot)\) \(\chi_{3997}(495,\cdot)\) \(\chi_{3997}(584,\cdot)\) \(\chi_{3997}(605,\cdot)\) \(\chi_{3997}(628,\cdot)\) \(\chi_{3997}(654,\cdot)\) \(\chi_{3997}(668,\cdot)\) \(\chi_{3997}(712,\cdot)\) \(\chi_{3997}(726,\cdot)\) \(\chi_{3997}(740,\cdot)\) \(\chi_{3997}(761,\cdot)\) \(\chi_{3997}(773,\cdot)\) \(\chi_{3997}(794,\cdot)\) \(\chi_{3997}(864,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{146}{285}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(668, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{129}{190}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{3}{190}\right)\) | \(e\left(\frac{39}{190}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{34}{95}\right)\) | \(e\left(\frac{103}{190}\right)\) | \(e\left(\frac{91}{95}\right)\) | \(e\left(\frac{139}{190}\right)\) |