Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fe
\(\chi_{3800}(89,\cdot)\) \(\chi_{3800}(129,\cdot)\) \(\chi_{3800}(409,\cdot)\) \(\chi_{3800}(489,\cdot)\) \(\chi_{3800}(889,\cdot)\) \(\chi_{3800}(1009,\cdot)\) \(\chi_{3800}(1169,\cdot)\) \(\chi_{3800}(1409,\cdot)\) \(\chi_{3800}(1609,\cdot)\) \(\chi_{3800}(1769,\cdot)\) \(\chi_{3800}(1929,\cdot)\) \(\chi_{3800}(2009,\cdot)\) \(\chi_{3800}(2169,\cdot)\) \(\chi_{3800}(2369,\cdot)\) \(\chi_{3800}(2409,\cdot)\) \(\chi_{3800}(2529,\cdot)\) \(\chi_{3800}(2689,\cdot)\) \(\chi_{3800}(2769,\cdot)\) \(\chi_{3800}(2929,\cdot)\) \(\chi_{3800}(3129,\cdot)\) \(\chi_{3800}(3169,\cdot)\) \(\chi_{3800}(3289,\cdot)\) \(\chi_{3800}(3529,\cdot)\) \(\chi_{3800}(3689,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((1,1,e\left(\frac{3}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{90}\right)\) |