Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(95\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{571}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.bw
\(\chi_{3997}(36,\cdot)\) \(\chi_{3997}(120,\cdot)\) \(\chi_{3997}(148,\cdot)\) \(\chi_{3997}(176,\cdot)\) \(\chi_{3997}(225,\cdot)\) \(\chi_{3997}(267,\cdot)\) \(\chi_{3997}(281,\cdot)\) \(\chi_{3997}(302,\cdot)\) \(\chi_{3997}(330,\cdot)\) \(\chi_{3997}(400,\cdot)\) \(\chi_{3997}(449,\cdot)\) \(\chi_{3997}(484,\cdot)\) \(\chi_{3997}(694,\cdot)\) \(\chi_{3997}(729,\cdot)\) \(\chi_{3997}(750,\cdot)\) \(\chi_{3997}(757,\cdot)\) \(\chi_{3997}(799,\cdot)\) \(\chi_{3997}(876,\cdot)\) \(\chi_{3997}(890,\cdot)\) \(\chi_{3997}(925,\cdot)\) \(\chi_{3997}(981,\cdot)\) \(\chi_{3997}(1002,\cdot)\) \(\chi_{3997}(1100,\cdot)\) \(\chi_{3997}(1135,\cdot)\) \(\chi_{3997}(1191,\cdot)\) \(\chi_{3997}(1198,\cdot)\) \(\chi_{3997}(1247,\cdot)\) \(\chi_{3997}(1296,\cdot)\) \(\chi_{3997}(1324,\cdot)\) \(\chi_{3997}(1331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 95 polynomial |
Values on generators
\((2285,1716)\) → \((1,e\left(\frac{87}{95}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{54}{95}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{12}{95}\right)\) |