Basic properties
| Modulus: | \(3025\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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.cz
\(\chi_{3025}(37,\cdot)\) \(\chi_{3025}(53,\cdot)\) \(\chi_{3025}(97,\cdot)\) \(\chi_{3025}(102,\cdot)\) \(\chi_{3025}(192,\cdot)\) \(\chi_{3025}(213,\cdot)\) \(\chi_{3025}(223,\cdot)\) \(\chi_{3025}(258,\cdot)\) \(\chi_{3025}(312,\cdot)\) \(\chi_{3025}(328,\cdot)\) \(\chi_{3025}(377,\cdot)\) \(\chi_{3025}(467,\cdot)\) \(\chi_{3025}(488,\cdot)\) \(\chi_{3025}(498,\cdot)\) \(\chi_{3025}(533,\cdot)\) \(\chi_{3025}(587,\cdot)\) \(\chi_{3025}(603,\cdot)\) \(\chi_{3025}(647,\cdot)\) \(\chi_{3025}(652,\cdot)\) \(\chi_{3025}(742,\cdot)\) \(\chi_{3025}(763,\cdot)\) \(\chi_{3025}(773,\cdot)\) \(\chi_{3025}(808,\cdot)\) \(\chi_{3025}(862,\cdot)\) \(\chi_{3025}(878,\cdot)\) \(\chi_{3025}(922,\cdot)\) \(\chi_{3025}(927,\cdot)\) \(\chi_{3025}(1017,\cdot)\) \(\chi_{3025}(1038,\cdot)\) \(\chi_{3025}(1048,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{21}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{183}{220}\right)\) | \(-i\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(-1\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{83}{110}\right)\) |