Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(1900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1900}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fi
\(\chi_{3800}(127,\cdot)\) \(\chi_{3800}(167,\cdot)\) \(\chi_{3800}(223,\cdot)\) \(\chi_{3800}(287,\cdot)\) \(\chi_{3800}(383,\cdot)\) \(\chi_{3800}(447,\cdot)\) \(\chi_{3800}(527,\cdot)\) \(\chi_{3800}(583,\cdot)\) \(\chi_{3800}(623,\cdot)\) \(\chi_{3800}(687,\cdot)\) \(\chi_{3800}(887,\cdot)\) \(\chi_{3800}(903,\cdot)\) \(\chi_{3800}(927,\cdot)\) \(\chi_{3800}(983,\cdot)\) \(\chi_{3800}(1047,\cdot)\) \(\chi_{3800}(1287,\cdot)\) \(\chi_{3800}(1383,\cdot)\) \(\chi_{3800}(1447,\cdot)\) \(\chi_{3800}(1503,\cdot)\) \(\chi_{3800}(1647,\cdot)\) \(\chi_{3800}(1663,\cdot)\) \(\chi_{3800}(1687,\cdot)\) \(\chi_{3800}(1903,\cdot)\) \(\chi_{3800}(1967,\cdot)\) \(\chi_{3800}(2047,\cdot)\) \(\chi_{3800}(2103,\cdot)\) \(\chi_{3800}(2263,\cdot)\) \(\chi_{3800}(2423,\cdot)\) \(\chi_{3800}(2447,\cdot)\) \(\chi_{3800}(2503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((-1,1,e\left(\frac{1}{20}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(127, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{37}{45}\right)\) |