Basic properties
| Modulus: | \(3025\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | 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.by
\(\chi_{3025}(56,\cdot)\) \(\chi_{3025}(111,\cdot)\) \(\chi_{3025}(166,\cdot)\) \(\chi_{3025}(221,\cdot)\) \(\chi_{3025}(331,\cdot)\) \(\chi_{3025}(386,\cdot)\) \(\chi_{3025}(441,\cdot)\) \(\chi_{3025}(496,\cdot)\) \(\chi_{3025}(661,\cdot)\) \(\chi_{3025}(716,\cdot)\) \(\chi_{3025}(771,\cdot)\) \(\chi_{3025}(881,\cdot)\) \(\chi_{3025}(936,\cdot)\) \(\chi_{3025}(991,\cdot)\) \(\chi_{3025}(1046,\cdot)\) \(\chi_{3025}(1156,\cdot)\) \(\chi_{3025}(1266,\cdot)\) \(\chi_{3025}(1321,\cdot)\) \(\chi_{3025}(1431,\cdot)\) \(\chi_{3025}(1486,\cdot)\) \(\chi_{3025}(1541,\cdot)\) \(\chi_{3025}(1596,\cdot)\) \(\chi_{3025}(1706,\cdot)\) \(\chi_{3025}(1761,\cdot)\) \(\chi_{3025}(1871,\cdot)\) \(\chi_{3025}(1981,\cdot)\) \(\chi_{3025}(2036,\cdot)\) \(\chi_{3025}(2091,\cdot)\) \(\chi_{3025}(2146,\cdot)\) \(\chi_{3025}(2256,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((727,2301)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) |