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.ex
\(\chi_{3800}(59,\cdot)\) \(\chi_{3800}(219,\cdot)\) \(\chi_{3800}(459,\cdot)\) \(\chi_{3800}(659,\cdot)\) \(\chi_{3800}(819,\cdot)\) \(\chi_{3800}(979,\cdot)\) \(\chi_{3800}(1059,\cdot)\) \(\chi_{3800}(1219,\cdot)\) \(\chi_{3800}(1419,\cdot)\) \(\chi_{3800}(1459,\cdot)\) \(\chi_{3800}(1579,\cdot)\) \(\chi_{3800}(1739,\cdot)\) \(\chi_{3800}(1819,\cdot)\) \(\chi_{3800}(1979,\cdot)\) \(\chi_{3800}(2179,\cdot)\) \(\chi_{3800}(2219,\cdot)\) \(\chi_{3800}(2339,\cdot)\) \(\chi_{3800}(2579,\cdot)\) \(\chi_{3800}(2739,\cdot)\) \(\chi_{3800}(2939,\cdot)\) \(\chi_{3800}(2979,\cdot)\) \(\chi_{3800}(3259,\cdot)\) \(\chi_{3800}(3339,\cdot)\) \(\chi_{3800}(3739,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{7}{10}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) |