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.ev
\(\chi_{3800}(139,\cdot)\) \(\chi_{3800}(339,\cdot)\) \(\chi_{3800}(579,\cdot)\) \(\chi_{3800}(739,\cdot)\) \(\chi_{3800}(859,\cdot)\) \(\chi_{3800}(1259,\cdot)\) \(\chi_{3800}(1339,\cdot)\) \(\chi_{3800}(1619,\cdot)\) \(\chi_{3800}(1659,\cdot)\) \(\chi_{3800}(1859,\cdot)\) \(\chi_{3800}(2019,\cdot)\) \(\chi_{3800}(2259,\cdot)\) \(\chi_{3800}(2379,\cdot)\) \(\chi_{3800}(2419,\cdot)\) \(\chi_{3800}(2619,\cdot)\) \(\chi_{3800}(2779,\cdot)\) \(\chi_{3800}(2859,\cdot)\) \(\chi_{3800}(3019,\cdot)\) \(\chi_{3800}(3139,\cdot)\) \(\chi_{3800}(3179,\cdot)\) \(\chi_{3800}(3379,\cdot)\) \(\chi_{3800}(3539,\cdot)\) \(\chi_{3800}(3619,\cdot)\) \(\chi_{3800}(3779,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{1}{10}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(2379, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{53}{90}\right)\) |