Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | 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.bp
\(\chi_{3971}(8,\cdot)\) \(\chi_{3971}(46,\cdot)\) \(\chi_{3971}(50,\cdot)\) \(\chi_{3971}(84,\cdot)\) \(\chi_{3971}(107,\cdot)\) \(\chi_{3971}(145,\cdot)\) \(\chi_{3971}(160,\cdot)\) \(\chi_{3971}(183,\cdot)\) \(\chi_{3971}(217,\cdot)\) \(\chi_{3971}(255,\cdot)\) \(\chi_{3971}(259,\cdot)\) \(\chi_{3971}(316,\cdot)\) \(\chi_{3971}(354,\cdot)\) \(\chi_{3971}(369,\cdot)\) \(\chi_{3971}(392,\cdot)\) \(\chi_{3971}(426,\cdot)\) \(\chi_{3971}(464,\cdot)\) \(\chi_{3971}(468,\cdot)\) \(\chi_{3971}(502,\cdot)\) \(\chi_{3971}(525,\cdot)\) \(\chi_{3971}(563,\cdot)\) \(\chi_{3971}(578,\cdot)\) \(\chi_{3971}(601,\cdot)\) \(\chi_{3971}(635,\cdot)\) \(\chi_{3971}(673,\cdot)\) \(\chi_{3971}(677,\cdot)\) \(\chi_{3971}(711,\cdot)\) \(\chi_{3971}(734,\cdot)\) \(\chi_{3971}(772,\cdot)\) \(\chi_{3971}(787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{88}{285}\right)\) | \(e\left(\frac{353}{570}\right)\) | \(e\left(\frac{176}{285}\right)\) | \(e\left(\frac{67}{285}\right)\) | \(e\left(\frac{529}{570}\right)\) | \(e\left(\frac{79}{190}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{68}{285}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) |