Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | 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.cl
\(\chi_{3997}(27,\cdot)\) \(\chi_{3997}(48,\cdot)\) \(\chi_{3997}(111,\cdot)\) \(\chi_{3997}(132,\cdot)\) \(\chi_{3997}(160,\cdot)\) \(\chi_{3997}(314,\cdot)\) \(\chi_{3997}(356,\cdot)\) \(\chi_{3997}(363,\cdot)\) \(\chi_{3997}(370,\cdot)\) \(\chi_{3997}(433,\cdot)\) \(\chi_{3997}(454,\cdot)\) \(\chi_{3997}(657,\cdot)\) \(\chi_{3997}(727,\cdot)\) \(\chi_{3997}(825,\cdot)\) \(\chi_{3997}(839,\cdot)\) \(\chi_{3997}(916,\cdot)\) \(\chi_{3997}(979,\cdot)\) \(\chi_{3997}(993,\cdot)\) \(\chi_{3997}(1000,\cdot)\) \(\chi_{3997}(1077,\cdot)\) \(\chi_{3997}(1091,\cdot)\) \(\chi_{3997}(1119,\cdot)\) \(\chi_{3997}(1168,\cdot)\) \(\chi_{3997}(1210,\cdot)\) \(\chi_{3997}(1308,\cdot)\) \(\chi_{3997}(1329,\cdot)\) \(\chi_{3997}(1336,\cdot)\) \(\chi_{3997}(1497,\cdot)\) \(\chi_{3997}(1567,\cdot)\) \(\chi_{3997}(1588,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((-1,e\left(\frac{1}{190}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{137}{190}\right)\) | \(e\left(\frac{71}{190}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{1}{95}\right)\) | \(e\left(\frac{56}{95}\right)\) | \(e\left(\frac{39}{95}\right)\) | \(e\left(\frac{23}{95}\right)\) |