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.cp
\(\chi_{3025}(19,\cdot)\) \(\chi_{3025}(29,\cdot)\) \(\chi_{3025}(189,\cdot)\) \(\chi_{3025}(259,\cdot)\) \(\chi_{3025}(294,\cdot)\) \(\chi_{3025}(304,\cdot)\) \(\chi_{3025}(464,\cdot)\) \(\chi_{3025}(534,\cdot)\) \(\chi_{3025}(569,\cdot)\) \(\chi_{3025}(579,\cdot)\) \(\chi_{3025}(739,\cdot)\) \(\chi_{3025}(809,\cdot)\) \(\chi_{3025}(854,\cdot)\) \(\chi_{3025}(1014,\cdot)\) \(\chi_{3025}(1084,\cdot)\) \(\chi_{3025}(1119,\cdot)\) \(\chi_{3025}(1289,\cdot)\) \(\chi_{3025}(1359,\cdot)\) \(\chi_{3025}(1394,\cdot)\) \(\chi_{3025}(1404,\cdot)\) \(\chi_{3025}(1634,\cdot)\) \(\chi_{3025}(1669,\cdot)\) \(\chi_{3025}(1679,\cdot)\) \(\chi_{3025}(1839,\cdot)\) \(\chi_{3025}(1944,\cdot)\) \(\chi_{3025}(1954,\cdot)\) \(\chi_{3025}(2114,\cdot)\) \(\chi_{3025}(2184,\cdot)\) \(\chi_{3025}(2219,\cdot)\) \(\chi_{3025}(2229,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) |