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.co
\(\chi_{3025}(54,\cdot)\) \(\chi_{3025}(109,\cdot)\) \(\chi_{3025}(164,\cdot)\) \(\chi_{3025}(219,\cdot)\) \(\chi_{3025}(329,\cdot)\) \(\chi_{3025}(384,\cdot)\) \(\chi_{3025}(439,\cdot)\) \(\chi_{3025}(494,\cdot)\) \(\chi_{3025}(659,\cdot)\) \(\chi_{3025}(714,\cdot)\) \(\chi_{3025}(769,\cdot)\) \(\chi_{3025}(879,\cdot)\) \(\chi_{3025}(934,\cdot)\) \(\chi_{3025}(989,\cdot)\) \(\chi_{3025}(1044,\cdot)\) \(\chi_{3025}(1154,\cdot)\) \(\chi_{3025}(1264,\cdot)\) \(\chi_{3025}(1319,\cdot)\) \(\chi_{3025}(1429,\cdot)\) \(\chi_{3025}(1484,\cdot)\) \(\chi_{3025}(1539,\cdot)\) \(\chi_{3025}(1594,\cdot)\) \(\chi_{3025}(1704,\cdot)\) \(\chi_{3025}(1759,\cdot)\) \(\chi_{3025}(1869,\cdot)\) \(\chi_{3025}(1979,\cdot)\) \(\chi_{3025}(2034,\cdot)\) \(\chi_{3025}(2089,\cdot)\) \(\chi_{3025}(2144,\cdot)\) \(\chi_{3025}(2254,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(54, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) |