Basic properties
| Modulus: | \(3025\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 3025.cm
\(\chi_{3025}(6,\cdot)\) \(\chi_{3025}(46,\cdot)\) \(\chi_{3025}(216,\cdot)\) \(\chi_{3025}(261,\cdot)\) \(\chi_{3025}(281,\cdot)\) \(\chi_{3025}(321,\cdot)\) \(\chi_{3025}(491,\cdot)\) \(\chi_{3025}(536,\cdot)\) \(\chi_{3025}(556,\cdot)\) \(\chi_{3025}(811,\cdot)\) \(\chi_{3025}(831,\cdot)\) \(\chi_{3025}(871,\cdot)\) \(\chi_{3025}(1041,\cdot)\) \(\chi_{3025}(1106,\cdot)\) \(\chi_{3025}(1146,\cdot)\) \(\chi_{3025}(1316,\cdot)\) \(\chi_{3025}(1361,\cdot)\) \(\chi_{3025}(1381,\cdot)\) \(\chi_{3025}(1421,\cdot)\) \(\chi_{3025}(1591,\cdot)\) \(\chi_{3025}(1636,\cdot)\) \(\chi_{3025}(1656,\cdot)\) \(\chi_{3025}(1696,\cdot)\) \(\chi_{3025}(1866,\cdot)\) \(\chi_{3025}(1911,\cdot)\) \(\chi_{3025}(1931,\cdot)\) \(\chi_{3025}(1971,\cdot)\) \(\chi_{3025}(2141,\cdot)\) \(\chi_{3025}(2186,\cdot)\) \(\chi_{3025}(2206,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{47}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(216, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{110}\right)\) | \(1\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(1\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{34}{55}\right)\) |