Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1710\) | 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.bu
\(\chi_{3971}(2,\cdot)\) \(\chi_{3971}(13,\cdot)\) \(\chi_{3971}(29,\cdot)\) \(\chi_{3971}(40,\cdot)\) \(\chi_{3971}(41,\cdot)\) \(\chi_{3971}(51,\cdot)\) \(\chi_{3971}(52,\cdot)\) \(\chi_{3971}(72,\cdot)\) \(\chi_{3971}(79,\cdot)\) \(\chi_{3971}(90,\cdot)\) \(\chi_{3971}(105,\cdot)\) \(\chi_{3971}(117,\cdot)\) \(\chi_{3971}(128,\cdot)\) \(\chi_{3971}(129,\cdot)\) \(\chi_{3971}(162,\cdot)\) \(\chi_{3971}(167,\cdot)\) \(\chi_{3971}(173,\cdot)\) \(\chi_{3971}(184,\cdot)\) \(\chi_{3971}(193,\cdot)\) \(\chi_{3971}(200,\cdot)\) \(\chi_{3971}(204,\cdot)\) \(\chi_{3971}(205,\cdot)\) \(\chi_{3971}(211,\cdot)\) \(\chi_{3971}(222,\cdot)\) \(\chi_{3971}(238,\cdot)\) \(\chi_{3971}(249,\cdot)\) \(\chi_{3971}(250,\cdot)\) \(\chi_{3971}(260,\cdot)\) \(\chi_{3971}(261,\cdot)\) \(\chi_{3971}(281,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 1710 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{17}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{641}{855}\right)\) | \(e\left(\frac{871}{1710}\right)\) | \(e\left(\frac{427}{855}\right)\) | \(e\left(\frac{284}{855}\right)\) | \(e\left(\frac{443}{1710}\right)\) | \(e\left(\frac{203}{570}\right)\) | \(e\left(\frac{71}{285}\right)\) | \(e\left(\frac{16}{855}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{1}{114}\right)\) |