Basic properties
| Modulus: | \(3025\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(24,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3025.cq
\(\chi_{3025}(24,\cdot)\) \(\chi_{3025}(74,\cdot)\) \(\chi_{3025}(149,\cdot)\) \(\chi_{3025}(249,\cdot)\) \(\chi_{3025}(299,\cdot)\) \(\chi_{3025}(349,\cdot)\) \(\chi_{3025}(424,\cdot)\) \(\chi_{3025}(574,\cdot)\) \(\chi_{3025}(624,\cdot)\) \(\chi_{3025}(799,\cdot)\) \(\chi_{3025}(849,\cdot)\) \(\chi_{3025}(899,\cdot)\) \(\chi_{3025}(974,\cdot)\) \(\chi_{3025}(1074,\cdot)\) \(\chi_{3025}(1124,\cdot)\) \(\chi_{3025}(1174,\cdot)\) \(\chi_{3025}(1249,\cdot)\) \(\chi_{3025}(1349,\cdot)\) \(\chi_{3025}(1399,\cdot)\) \(\chi_{3025}(1524,\cdot)\) \(\chi_{3025}(1624,\cdot)\) \(\chi_{3025}(1674,\cdot)\) \(\chi_{3025}(1724,\cdot)\) \(\chi_{3025}(1799,\cdot)\) \(\chi_{3025}(1899,\cdot)\) \(\chi_{3025}(1949,\cdot)\) \(\chi_{3025}(1999,\cdot)\) \(\chi_{3025}(2074,\cdot)\) \(\chi_{3025}(2174,\cdot)\) \(\chi_{3025}(2224,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((-1,e\left(\frac{91}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(24, a) \) | \(-1\) | \(1\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) |