Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(1900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1900}(119,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.eu
\(\chi_{3800}(119,\cdot)\) \(\chi_{3800}(359,\cdot)\) \(\chi_{3800}(479,\cdot)\) \(\chi_{3800}(519,\cdot)\) \(\chi_{3800}(719,\cdot)\) \(\chi_{3800}(879,\cdot)\) \(\chi_{3800}(959,\cdot)\) \(\chi_{3800}(1119,\cdot)\) \(\chi_{3800}(1239,\cdot)\) \(\chi_{3800}(1279,\cdot)\) \(\chi_{3800}(1479,\cdot)\) \(\chi_{3800}(1639,\cdot)\) \(\chi_{3800}(1719,\cdot)\) \(\chi_{3800}(1879,\cdot)\) \(\chi_{3800}(2039,\cdot)\) \(\chi_{3800}(2239,\cdot)\) \(\chi_{3800}(2479,\cdot)\) \(\chi_{3800}(2639,\cdot)\) \(\chi_{3800}(2759,\cdot)\) \(\chi_{3800}(3159,\cdot)\) \(\chi_{3800}(3239,\cdot)\) \(\chi_{3800}(3519,\cdot)\) \(\chi_{3800}(3559,\cdot)\) \(\chi_{3800}(3759,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,1,e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(119, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{41}{45}\right)\) |