Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(285\) | 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 9025.cb
\(\chi_{9025}(11,\cdot)\) \(\chi_{9025}(106,\cdot)\) \(\chi_{9025}(121,\cdot)\) \(\chi_{9025}(216,\cdot)\) \(\chi_{9025}(296,\cdot)\) \(\chi_{9025}(311,\cdot)\) \(\chi_{9025}(391,\cdot)\) \(\chi_{9025}(406,\cdot)\) \(\chi_{9025}(486,\cdot)\) \(\chi_{9025}(581,\cdot)\) \(\chi_{9025}(596,\cdot)\) \(\chi_{9025}(691,\cdot)\) \(\chi_{9025}(771,\cdot)\) \(\chi_{9025}(786,\cdot)\) \(\chi_{9025}(866,\cdot)\) \(\chi_{9025}(881,\cdot)\) \(\chi_{9025}(961,\cdot)\) \(\chi_{9025}(1056,\cdot)\) \(\chi_{9025}(1071,\cdot)\) \(\chi_{9025}(1166,\cdot)\) \(\chi_{9025}(1246,\cdot)\) \(\chi_{9025}(1261,\cdot)\) \(\chi_{9025}(1341,\cdot)\) \(\chi_{9025}(1356,\cdot)\) \(\chi_{9025}(1436,\cdot)\) \(\chi_{9025}(1531,\cdot)\) \(\chi_{9025}(1546,\cdot)\) \(\chi_{9025}(1641,\cdot)\) \(\chi_{9025}(1721,\cdot)\) \(\chi_{9025}(1816,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 285 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{17}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{285}\right)\) | \(e\left(\frac{16}{285}\right)\) | \(e\left(\frac{56}{285}\right)\) | \(e\left(\frac{44}{285}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{32}{285}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{92}{285}\right)\) |