Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(855\) | 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.bs
\(\chi_{3971}(4,\cdot)\) \(\chi_{3971}(5,\cdot)\) \(\chi_{3971}(9,\cdot)\) \(\chi_{3971}(16,\cdot)\) \(\chi_{3971}(25,\cdot)\) \(\chi_{3971}(36,\cdot)\) \(\chi_{3971}(42,\cdot)\) \(\chi_{3971}(47,\cdot)\) \(\chi_{3971}(80,\cdot)\) \(\chi_{3971}(81,\cdot)\) \(\chi_{3971}(82,\cdot)\) \(\chi_{3971}(92,\cdot)\) \(\chi_{3971}(93,\cdot)\) \(\chi_{3971}(104,\cdot)\) \(\chi_{3971}(119,\cdot)\) \(\chi_{3971}(130,\cdot)\) \(\chi_{3971}(137,\cdot)\) \(\chi_{3971}(157,\cdot)\) \(\chi_{3971}(158,\cdot)\) \(\chi_{3971}(168,\cdot)\) \(\chi_{3971}(169,\cdot)\) \(\chi_{3971}(180,\cdot)\) \(\chi_{3971}(196,\cdot)\) \(\chi_{3971}(207,\cdot)\) \(\chi_{3971}(213,\cdot)\) \(\chi_{3971}(214,\cdot)\) \(\chi_{3971}(218,\cdot)\) \(\chi_{3971}(225,\cdot)\) \(\chi_{3971}(251,\cdot)\) \(\chi_{3971}(256,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 855 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{176}{855}\right)\) | \(e\left(\frac{353}{855}\right)\) | \(e\left(\frac{352}{855}\right)\) | \(e\left(\frac{134}{855}\right)\) | \(e\left(\frac{529}{855}\right)\) | \(e\left(\frac{79}{285}\right)\) | \(e\left(\frac{176}{285}\right)\) | \(e\left(\frac{706}{855}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{47}{57}\right)\) |