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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.ff
\(\chi_{3800}(131,\cdot)\) \(\chi_{3800}(291,\cdot)\) \(\chi_{3800}(491,\cdot)\) \(\chi_{3800}(731,\cdot)\) \(\chi_{3800}(891,\cdot)\) \(\chi_{3800}(1011,\cdot)\) \(\chi_{3800}(1411,\cdot)\) \(\chi_{3800}(1491,\cdot)\) \(\chi_{3800}(1771,\cdot)\) \(\chi_{3800}(1811,\cdot)\) \(\chi_{3800}(2011,\cdot)\) \(\chi_{3800}(2171,\cdot)\) \(\chi_{3800}(2411,\cdot)\) \(\chi_{3800}(2531,\cdot)\) \(\chi_{3800}(2571,\cdot)\) \(\chi_{3800}(2771,\cdot)\) \(\chi_{3800}(2931,\cdot)\) \(\chi_{3800}(3011,\cdot)\) \(\chi_{3800}(3171,\cdot)\) \(\chi_{3800}(3291,\cdot)\) \(\chi_{3800}(3331,\cdot)\) \(\chi_{3800}(3531,\cdot)\) \(\chi_{3800}(3691,\cdot)\) \(\chi_{3800}(3771,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(131, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) |