Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.ci
\(\chi_{9025}(31,\cdot)\) \(\chi_{9025}(46,\cdot)\) \(\chi_{9025}(141,\cdot)\) \(\chi_{9025}(221,\cdot)\) \(\chi_{9025}(236,\cdot)\) \(\chi_{9025}(316,\cdot)\) \(\chi_{9025}(331,\cdot)\) \(\chi_{9025}(411,\cdot)\) \(\chi_{9025}(506,\cdot)\) \(\chi_{9025}(521,\cdot)\) \(\chi_{9025}(616,\cdot)\) \(\chi_{9025}(696,\cdot)\) \(\chi_{9025}(711,\cdot)\) \(\chi_{9025}(806,\cdot)\) \(\chi_{9025}(886,\cdot)\) \(\chi_{9025}(981,\cdot)\) \(\chi_{9025}(996,\cdot)\) \(\chi_{9025}(1091,\cdot)\) \(\chi_{9025}(1171,\cdot)\) \(\chi_{9025}(1186,\cdot)\) \(\chi_{9025}(1266,\cdot)\) \(\chi_{9025}(1281,\cdot)\) \(\chi_{9025}(1361,\cdot)\) \(\chi_{9025}(1456,\cdot)\) \(\chi_{9025}(1471,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{49}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{570}\right)\) | \(e\left(\frac{539}{570}\right)\) | \(e\left(\frac{17}{285}\right)\) | \(e\left(\frac{278}{285}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{17}{190}\right)\) | \(e\left(\frac{254}{285}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{1}{190}\right)\) | \(e\left(\frac{463}{570}\right)\) |