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.cr
\(\chi_{3025}(39,\cdot)\) \(\chi_{3025}(129,\cdot)\) \(\chi_{3025}(134,\cdot)\) \(\chi_{3025}(194,\cdot)\) \(\chi_{3025}(314,\cdot)\) \(\chi_{3025}(404,\cdot)\) \(\chi_{3025}(409,\cdot)\) \(\chi_{3025}(469,\cdot)\) \(\chi_{3025}(589,\cdot)\) \(\chi_{3025}(679,\cdot)\) \(\chi_{3025}(684,\cdot)\) \(\chi_{3025}(744,\cdot)\) \(\chi_{3025}(864,\cdot)\) \(\chi_{3025}(954,\cdot)\) \(\chi_{3025}(1019,\cdot)\) \(\chi_{3025}(1139,\cdot)\) \(\chi_{3025}(1229,\cdot)\) \(\chi_{3025}(1234,\cdot)\) \(\chi_{3025}(1294,\cdot)\) \(\chi_{3025}(1414,\cdot)\) \(\chi_{3025}(1504,\cdot)\) \(\chi_{3025}(1509,\cdot)\) \(\chi_{3025}(1569,\cdot)\) \(\chi_{3025}(1689,\cdot)\) \(\chi_{3025}(1779,\cdot)\) \(\chi_{3025}(1784,\cdot)\) \(\chi_{3025}(1844,\cdot)\) \(\chi_{3025}(1964,\cdot)\) \(\chi_{3025}(2059,\cdot)\) \(\chi_{3025}(2119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{79}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) |