Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | 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 3971.bn
\(\chi_{3971}(10,\cdot)\) \(\chi_{3971}(21,\cdot)\) \(\chi_{3971}(32,\cdot)\) \(\chi_{3971}(98,\cdot)\) \(\chi_{3971}(109,\cdot)\) \(\chi_{3971}(186,\cdot)\) \(\chi_{3971}(219,\cdot)\) \(\chi_{3971}(230,\cdot)\) \(\chi_{3971}(241,\cdot)\) \(\chi_{3971}(318,\cdot)\) \(\chi_{3971}(395,\cdot)\) \(\chi_{3971}(428,\cdot)\) \(\chi_{3971}(439,\cdot)\) \(\chi_{3971}(450,\cdot)\) \(\chi_{3971}(516,\cdot)\) \(\chi_{3971}(527,\cdot)\) \(\chi_{3971}(604,\cdot)\) \(\chi_{3971}(637,\cdot)\) \(\chi_{3971}(648,\cdot)\) \(\chi_{3971}(659,\cdot)\) \(\chi_{3971}(725,\cdot)\) \(\chi_{3971}(736,\cdot)\) \(\chi_{3971}(813,\cdot)\) \(\chi_{3971}(846,\cdot)\) \(\chi_{3971}(857,\cdot)\) \(\chi_{3971}(868,\cdot)\) \(\chi_{3971}(934,\cdot)\) \(\chi_{3971}(945,\cdot)\) \(\chi_{3971}(1022,\cdot)\) \(\chi_{3971}(1066,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((-1,e\left(\frac{5}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{88}{171}\right)\) | \(e\left(\frac{11}{342}\right)\) | \(e\left(\frac{5}{171}\right)\) | \(e\left(\frac{67}{171}\right)\) | \(e\left(\frac{187}{342}\right)\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{155}{171}\right)\) | \(e\left(\frac{7}{114}\right)\) |