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.ev
\(\chi_{3311}(97,\cdot)\) \(\chi_{3311}(279,\cdot)\) \(\chi_{3311}(489,\cdot)\) \(\chi_{3311}(643,\cdot)\) \(\chi_{3311}(790,\cdot)\) \(\chi_{3311}(895,\cdot)\) \(\chi_{3311}(944,\cdot)\) \(\chi_{3311}(993,\cdot)\) \(\chi_{3311}(1182,\cdot)\) \(\chi_{3311}(1301,\cdot)\) \(\chi_{3311}(1483,\cdot)\) \(\chi_{3311}(1798,\cdot)\) \(\chi_{3311}(1896,\cdot)\) \(\chi_{3311}(1994,\cdot)\) \(\chi_{3311}(2099,\cdot)\) \(\chi_{3311}(2148,\cdot)\) \(\chi_{3311}(2204,\cdot)\) \(\chi_{3311}(2687,\cdot)\) \(\chi_{3311}(2799,\cdot)\) \(\chi_{3311}(2897,\cdot)\) \(\chi_{3311}(3051,\cdot)\) \(\chi_{3311}(3100,\cdot)\) \(\chi_{3311}(3107,\cdot)\) \(\chi_{3311}(3303,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1893,904,2927)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{67}{70}\right)\) |