Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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.fc
\(\chi_{3800}(91,\cdot)\) \(\chi_{3800}(211,\cdot)\) \(\chi_{3800}(371,\cdot)\) \(\chi_{3800}(611,\cdot)\) \(\chi_{3800}(811,\cdot)\) \(\chi_{3800}(971,\cdot)\) \(\chi_{3800}(1131,\cdot)\) \(\chi_{3800}(1211,\cdot)\) \(\chi_{3800}(1371,\cdot)\) \(\chi_{3800}(1571,\cdot)\) \(\chi_{3800}(1611,\cdot)\) \(\chi_{3800}(1731,\cdot)\) \(\chi_{3800}(1891,\cdot)\) \(\chi_{3800}(1971,\cdot)\) \(\chi_{3800}(2131,\cdot)\) \(\chi_{3800}(2331,\cdot)\) \(\chi_{3800}(2371,\cdot)\) \(\chi_{3800}(2491,\cdot)\) \(\chi_{3800}(2731,\cdot)\) \(\chi_{3800}(2891,\cdot)\) \(\chi_{3800}(3091,\cdot)\) \(\chi_{3800}(3131,\cdot)\) \(\chi_{3800}(3411,\cdot)\) \(\chi_{3800}(3491,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{1}{5}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{45}\right)\) |