Basic properties
| Modulus: | \(3311\) | |
| Conductor: | \(3311\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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 3311.ex
\(\chi_{3311}(118,\cdot)\) \(\chi_{3311}(237,\cdot)\) \(\chi_{3311}(426,\cdot)\) \(\chi_{3311}(475,\cdot)\) \(\chi_{3311}(524,\cdot)\) \(\chi_{3311}(629,\cdot)\) \(\chi_{3311}(776,\cdot)\) \(\chi_{3311}(930,\cdot)\) \(\chi_{3311}(1140,\cdot)\) \(\chi_{3311}(1322,\cdot)\) \(\chi_{3311}(1427,\cdot)\) \(\chi_{3311}(1623,\cdot)\) \(\chi_{3311}(1630,\cdot)\) \(\chi_{3311}(1679,\cdot)\) \(\chi_{3311}(1833,\cdot)\) \(\chi_{3311}(1931,\cdot)\) \(\chi_{3311}(2043,\cdot)\) \(\chi_{3311}(2526,\cdot)\) \(\chi_{3311}(2582,\cdot)\) \(\chi_{3311}(2631,\cdot)\) \(\chi_{3311}(2736,\cdot)\) \(\chi_{3311}(2834,\cdot)\) \(\chi_{3311}(2932,\cdot)\) \(\chi_{3311}(3247,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1893,904,2927)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(1140, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{22}{35}\right)\) |