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.cf
\(\chi_{3025}(116,\cdot)\) \(\chi_{3025}(206,\cdot)\) \(\chi_{3025}(211,\cdot)\) \(\chi_{3025}(271,\cdot)\) \(\chi_{3025}(391,\cdot)\) \(\chi_{3025}(486,\cdot)\) \(\chi_{3025}(546,\cdot)\) \(\chi_{3025}(666,\cdot)\) \(\chi_{3025}(756,\cdot)\) \(\chi_{3025}(761,\cdot)\) \(\chi_{3025}(821,\cdot)\) \(\chi_{3025}(1031,\cdot)\) \(\chi_{3025}(1036,\cdot)\) \(\chi_{3025}(1096,\cdot)\) \(\chi_{3025}(1216,\cdot)\) \(\chi_{3025}(1306,\cdot)\) \(\chi_{3025}(1311,\cdot)\) \(\chi_{3025}(1491,\cdot)\) \(\chi_{3025}(1581,\cdot)\) \(\chi_{3025}(1586,\cdot)\) \(\chi_{3025}(1646,\cdot)\) \(\chi_{3025}(1766,\cdot)\) \(\chi_{3025}(1856,\cdot)\) \(\chi_{3025}(1861,\cdot)\) \(\chi_{3025}(1921,\cdot)\) \(\chi_{3025}(2041,\cdot)\) \(\chi_{3025}(2131,\cdot)\) \(\chi_{3025}(2136,\cdot)\) \(\chi_{3025}(2196,\cdot)\) \(\chi_{3025}(2316,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{21}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(1311, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) |