Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1805}(24,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.cc
\(\chi_{9025}(24,\cdot)\) \(\chi_{9025}(74,\cdot)\) \(\chi_{9025}(149,\cdot)\) \(\chi_{9025}(199,\cdot)\) \(\chi_{9025}(424,\cdot)\) \(\chi_{9025}(499,\cdot)\) \(\chi_{9025}(549,\cdot)\) \(\chi_{9025}(574,\cdot)\) \(\chi_{9025}(624,\cdot)\) \(\chi_{9025}(674,\cdot)\) \(\chi_{9025}(899,\cdot)\) \(\chi_{9025}(974,\cdot)\) \(\chi_{9025}(1024,\cdot)\) \(\chi_{9025}(1049,\cdot)\) \(\chi_{9025}(1099,\cdot)\) \(\chi_{9025}(1149,\cdot)\) \(\chi_{9025}(1374,\cdot)\) \(\chi_{9025}(1449,\cdot)\) \(\chi_{9025}(1499,\cdot)\) \(\chi_{9025}(1524,\cdot)\) \(\chi_{9025}(1574,\cdot)\) \(\chi_{9025}(1624,\cdot)\) \(\chi_{9025}(1849,\cdot)\) \(\chi_{9025}(1924,\cdot)\) \(\chi_{9025}(1974,\cdot)\) \(\chi_{9025}(1999,\cdot)\) \(\chi_{9025}(2049,\cdot)\) \(\chi_{9025}(2099,\cdot)\) \(\chi_{9025}(2324,\cdot)\) \(\chi_{9025}(2399,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((-1,e\left(\frac{71}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{342}\right)\) | \(e\left(\frac{73}{342}\right)\) | \(e\left(\frac{142}{171}\right)\) | \(e\left(\frac{22}{171}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{35}{342}\right)\) |