Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3971.bo
\(\chi_{3971}(34,\cdot)\) \(\chi_{3971}(67,\cdot)\) \(\chi_{3971}(78,\cdot)\) \(\chi_{3971}(89,\cdot)\) \(\chi_{3971}(155,\cdot)\) \(\chi_{3971}(166,\cdot)\) \(\chi_{3971}(243,\cdot)\) \(\chi_{3971}(276,\cdot)\) \(\chi_{3971}(287,\cdot)\) \(\chi_{3971}(298,\cdot)\) \(\chi_{3971}(364,\cdot)\) \(\chi_{3971}(375,\cdot)\) \(\chi_{3971}(452,\cdot)\) \(\chi_{3971}(485,\cdot)\) \(\chi_{3971}(496,\cdot)\) \(\chi_{3971}(507,\cdot)\) \(\chi_{3971}(573,\cdot)\) \(\chi_{3971}(584,\cdot)\) \(\chi_{3971}(661,\cdot)\) \(\chi_{3971}(705,\cdot)\) \(\chi_{3971}(716,\cdot)\) \(\chi_{3971}(782,\cdot)\) \(\chi_{3971}(793,\cdot)\) \(\chi_{3971}(870,\cdot)\) \(\chi_{3971}(903,\cdot)\) \(\chi_{3971}(914,\cdot)\) \(\chi_{3971}(925,\cdot)\) \(\chi_{3971}(991,\cdot)\) \(\chi_{3971}(1002,\cdot)\) \(\chi_{3971}(1079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((1,e\left(\frac{227}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{227}{342}\right)\) | \(e\left(\frac{89}{342}\right)\) | \(e\left(\frac{56}{171}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{158}{171}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{223}{342}\right)\) | \(e\left(\frac{67}{114}\right)\) |