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.cd
\(\chi_{3025}(14,\cdot)\) \(\chi_{3025}(59,\cdot)\) \(\chi_{3025}(229,\cdot)\) \(\chi_{3025}(289,\cdot)\) \(\chi_{3025}(334,\cdot)\) \(\chi_{3025}(504,\cdot)\) \(\chi_{3025}(544,\cdot)\) \(\chi_{3025}(564,\cdot)\) \(\chi_{3025}(609,\cdot)\) \(\chi_{3025}(779,\cdot)\) \(\chi_{3025}(819,\cdot)\) \(\chi_{3025}(839,\cdot)\) \(\chi_{3025}(884,\cdot)\) \(\chi_{3025}(1054,\cdot)\) \(\chi_{3025}(1094,\cdot)\) \(\chi_{3025}(1114,\cdot)\) \(\chi_{3025}(1159,\cdot)\) \(\chi_{3025}(1329,\cdot)\) \(\chi_{3025}(1369,\cdot)\) \(\chi_{3025}(1389,\cdot)\) \(\chi_{3025}(1434,\cdot)\) \(\chi_{3025}(1604,\cdot)\) \(\chi_{3025}(1644,\cdot)\) \(\chi_{3025}(1664,\cdot)\) \(\chi_{3025}(1709,\cdot)\) \(\chi_{3025}(1879,\cdot)\) \(\chi_{3025}(1919,\cdot)\) \(\chi_{3025}(1984,\cdot)\) \(\chi_{3025}(2154,\cdot)\) \(\chi_{3025}(2194,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{49}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{110}\right)\) | \(-1\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(1\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{51}{55}\right)\) |