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.ca
\(\chi_{3025}(16,\cdot)\) \(\chi_{3025}(86,\cdot)\) \(\chi_{3025}(246,\cdot)\) \(\chi_{3025}(256,\cdot)\) \(\chi_{3025}(291,\cdot)\) \(\chi_{3025}(361,\cdot)\) \(\chi_{3025}(521,\cdot)\) \(\chi_{3025}(531,\cdot)\) \(\chi_{3025}(566,\cdot)\) \(\chi_{3025}(636,\cdot)\) \(\chi_{3025}(796,\cdot)\) \(\chi_{3025}(806,\cdot)\) \(\chi_{3025}(841,\cdot)\) \(\chi_{3025}(911,\cdot)\) \(\chi_{3025}(1071,\cdot)\) \(\chi_{3025}(1081,\cdot)\) \(\chi_{3025}(1186,\cdot)\) \(\chi_{3025}(1346,\cdot)\) \(\chi_{3025}(1356,\cdot)\) \(\chi_{3025}(1391,\cdot)\) \(\chi_{3025}(1621,\cdot)\) \(\chi_{3025}(1631,\cdot)\) \(\chi_{3025}(1666,\cdot)\) \(\chi_{3025}(1736,\cdot)\) \(\chi_{3025}(1906,\cdot)\) \(\chi_{3025}(1941,\cdot)\) \(\chi_{3025}(2011,\cdot)\) \(\chi_{3025}(2171,\cdot)\) \(\chi_{3025}(2216,\cdot)\) \(\chi_{3025}(2286,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((727,2301)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{43}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(636, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) |