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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3025.cj
\(\chi_{3025}(4,\cdot)\) \(\chi_{3025}(64,\cdot)\) \(\chi_{3025}(69,\cdot)\) \(\chi_{3025}(159,\cdot)\) \(\chi_{3025}(279,\cdot)\) \(\chi_{3025}(339,\cdot)\) \(\chi_{3025}(344,\cdot)\) \(\chi_{3025}(434,\cdot)\) \(\chi_{3025}(554,\cdot)\) \(\chi_{3025}(619,\cdot)\) \(\chi_{3025}(709,\cdot)\) \(\chi_{3025}(829,\cdot)\) \(\chi_{3025}(889,\cdot)\) \(\chi_{3025}(894,\cdot)\) \(\chi_{3025}(984,\cdot)\) \(\chi_{3025}(1104,\cdot)\) \(\chi_{3025}(1164,\cdot)\) \(\chi_{3025}(1169,\cdot)\) \(\chi_{3025}(1259,\cdot)\) \(\chi_{3025}(1379,\cdot)\) \(\chi_{3025}(1439,\cdot)\) \(\chi_{3025}(1444,\cdot)\) \(\chi_{3025}(1534,\cdot)\) \(\chi_{3025}(1714,\cdot)\) \(\chi_{3025}(1719,\cdot)\) \(\chi_{3025}(1809,\cdot)\) \(\chi_{3025}(1929,\cdot)\) \(\chi_{3025}(1989,\cdot)\) \(\chi_{3025}(1994,\cdot)\) \(\chi_{3025}(2204,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) |