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.cn
\(\chi_{1900}(71,\cdot)\) \(\chi_{1900}(91,\cdot)\) \(\chi_{1900}(211,\cdot)\) \(\chi_{1900}(231,\cdot)\) \(\chi_{1900}(371,\cdot)\) \(\chi_{1900}(431,\cdot)\) \(\chi_{1900}(471,\cdot)\) \(\chi_{1900}(591,\cdot)\) \(\chi_{1900}(611,\cdot)\) \(\chi_{1900}(811,\cdot)\) \(\chi_{1900}(831,\cdot)\) \(\chi_{1900}(971,\cdot)\) \(\chi_{1900}(991,\cdot)\) \(\chi_{1900}(1131,\cdot)\) \(\chi_{1900}(1191,\cdot)\) \(\chi_{1900}(1211,\cdot)\) \(\chi_{1900}(1231,\cdot)\) \(\chi_{1900}(1371,\cdot)\) \(\chi_{1900}(1511,\cdot)\) \(\chi_{1900}(1571,\cdot)\) \(\chi_{1900}(1591,\cdot)\) \(\chi_{1900}(1611,\cdot)\) \(\chi_{1900}(1731,\cdot)\) \(\chi_{1900}(1891,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,77,401)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{73}{90}\right)\) |