Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fm
\(\chi_{3800}(3,\cdot)\) \(\chi_{3800}(67,\cdot)\) \(\chi_{3800}(147,\cdot)\) \(\chi_{3800}(203,\cdot)\) \(\chi_{3800}(363,\cdot)\) \(\chi_{3800}(523,\cdot)\) \(\chi_{3800}(547,\cdot)\) \(\chi_{3800}(603,\cdot)\) \(\chi_{3800}(667,\cdot)\) \(\chi_{3800}(763,\cdot)\) \(\chi_{3800}(827,\cdot)\) \(\chi_{3800}(963,\cdot)\) \(\chi_{3800}(1003,\cdot)\) \(\chi_{3800}(1067,\cdot)\) \(\chi_{3800}(1123,\cdot)\) \(\chi_{3800}(1267,\cdot)\) \(\chi_{3800}(1283,\cdot)\) \(\chi_{3800}(1363,\cdot)\) \(\chi_{3800}(1427,\cdot)\) \(\chi_{3800}(1523,\cdot)\) \(\chi_{3800}(1587,\cdot)\) \(\chi_{3800}(1667,\cdot)\) \(\chi_{3800}(1723,\cdot)\) \(\chi_{3800}(1763,\cdot)\) \(\chi_{3800}(1827,\cdot)\) \(\chi_{3800}(1883,\cdot)\) \(\chi_{3800}(2027,\cdot)\) \(\chi_{3800}(2067,\cdot)\) \(\chi_{3800}(2123,\cdot)\) \(\chi_{3800}(2187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{7}{20}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{151}{180}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{43}{90}\right)\) |