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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3025.cg
\(\chi_{3025}(21,\cdot)\) \(\chi_{3025}(131,\cdot)\) \(\chi_{3025}(186,\cdot)\) \(\chi_{3025}(296,\cdot)\) \(\chi_{3025}(406,\cdot)\) \(\chi_{3025}(461,\cdot)\) \(\chi_{3025}(516,\cdot)\) \(\chi_{3025}(571,\cdot)\) \(\chi_{3025}(681,\cdot)\) \(\chi_{3025}(736,\cdot)\) \(\chi_{3025}(791,\cdot)\) \(\chi_{3025}(956,\cdot)\) \(\chi_{3025}(1011,\cdot)\) \(\chi_{3025}(1066,\cdot)\) \(\chi_{3025}(1121,\cdot)\) \(\chi_{3025}(1231,\cdot)\) \(\chi_{3025}(1286,\cdot)\) \(\chi_{3025}(1341,\cdot)\) \(\chi_{3025}(1396,\cdot)\) \(\chi_{3025}(1506,\cdot)\) \(\chi_{3025}(1561,\cdot)\) \(\chi_{3025}(1616,\cdot)\) \(\chi_{3025}(1671,\cdot)\) \(\chi_{3025}(1781,\cdot)\) \(\chi_{3025}(1836,\cdot)\) \(\chi_{3025}(1891,\cdot)\) \(\chi_{3025}(1946,\cdot)\) \(\chi_{3025}(2111,\cdot)\) \(\chi_{3025}(2166,\cdot)\) \(\chi_{3025}(2221,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) |