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.ct
\(\chi_{3025}(104,\cdot)\) \(\chi_{3025}(114,\cdot)\) \(\chi_{3025}(119,\cdot)\) \(\chi_{3025}(234,\cdot)\) \(\chi_{3025}(379,\cdot)\) \(\chi_{3025}(389,\cdot)\) \(\chi_{3025}(394,\cdot)\) \(\chi_{3025}(509,\cdot)\) \(\chi_{3025}(654,\cdot)\) \(\chi_{3025}(664,\cdot)\) \(\chi_{3025}(669,\cdot)\) \(\chi_{3025}(784,\cdot)\) \(\chi_{3025}(929,\cdot)\) \(\chi_{3025}(939,\cdot)\) \(\chi_{3025}(944,\cdot)\) \(\chi_{3025}(1059,\cdot)\) \(\chi_{3025}(1204,\cdot)\) \(\chi_{3025}(1214,\cdot)\) \(\chi_{3025}(1489,\cdot)\) \(\chi_{3025}(1494,\cdot)\) \(\chi_{3025}(1609,\cdot)\) \(\chi_{3025}(1754,\cdot)\) \(\chi_{3025}(1764,\cdot)\) \(\chi_{3025}(1769,\cdot)\) \(\chi_{3025}(1884,\cdot)\) \(\chi_{3025}(2029,\cdot)\) \(\chi_{3025}(2039,\cdot)\) \(\chi_{3025}(2044,\cdot)\) \(\chi_{3025}(2159,\cdot)\) \(\chi_{3025}(2304,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{12}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(929, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) |