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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fk
\(\chi_{3800}(123,\cdot)\) \(\chi_{3800}(187,\cdot)\) \(\chi_{3800}(283,\cdot)\) \(\chi_{3800}(347,\cdot)\) \(\chi_{3800}(403,\cdot)\) \(\chi_{3800}(427,\cdot)\) \(\chi_{3800}(587,\cdot)\) \(\chi_{3800}(747,\cdot)\) \(\chi_{3800}(803,\cdot)\) \(\chi_{3800}(883,\cdot)\) \(\chi_{3800}(947,\cdot)\) \(\chi_{3800}(1163,\cdot)\) \(\chi_{3800}(1187,\cdot)\) \(\chi_{3800}(1203,\cdot)\) \(\chi_{3800}(1347,\cdot)\) \(\chi_{3800}(1403,\cdot)\) \(\chi_{3800}(1467,\cdot)\) \(\chi_{3800}(1563,\cdot)\) \(\chi_{3800}(1803,\cdot)\) \(\chi_{3800}(1867,\cdot)\) \(\chi_{3800}(1923,\cdot)\) \(\chi_{3800}(1947,\cdot)\) \(\chi_{3800}(1963,\cdot)\) \(\chi_{3800}(2163,\cdot)\) \(\chi_{3800}(2227,\cdot)\) \(\chi_{3800}(2267,\cdot)\) \(\chi_{3800}(2323,\cdot)\) \(\chi_{3800}(2403,\cdot)\) \(\chi_{3800}(2467,\cdot)\) \(\chi_{3800}(2563,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{7}{20}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(1203, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{45}\right)\) |