Basic properties
| Modulus: | \(1900\) | |
| Conductor: | \(1900\) | 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 1900.cj
\(\chi_{1900}(59,\cdot)\) \(\chi_{1900}(79,\cdot)\) \(\chi_{1900}(219,\cdot)\) \(\chi_{1900}(279,\cdot)\) \(\chi_{1900}(319,\cdot)\) \(\chi_{1900}(439,\cdot)\) \(\chi_{1900}(459,\cdot)\) \(\chi_{1900}(659,\cdot)\) \(\chi_{1900}(679,\cdot)\) \(\chi_{1900}(819,\cdot)\) \(\chi_{1900}(839,\cdot)\) \(\chi_{1900}(979,\cdot)\) \(\chi_{1900}(1039,\cdot)\) \(\chi_{1900}(1059,\cdot)\) \(\chi_{1900}(1079,\cdot)\) \(\chi_{1900}(1219,\cdot)\) \(\chi_{1900}(1359,\cdot)\) \(\chi_{1900}(1419,\cdot)\) \(\chi_{1900}(1439,\cdot)\) \(\chi_{1900}(1459,\cdot)\) \(\chi_{1900}(1579,\cdot)\) \(\chi_{1900}(1739,\cdot)\) \(\chi_{1900}(1819,\cdot)\) \(\chi_{1900}(1839,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,77,401)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(279, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{83}{90}\right)\) |