Basic properties
| Modulus: | \(3311\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{473}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3311.et
\(\chi_{3311}(127,\cdot)\) \(\chi_{3311}(183,\cdot)\) \(\chi_{3311}(365,\cdot)\) \(\chi_{3311}(666,\cdot)\) \(\chi_{3311}(778,\cdot)\) \(\chi_{3311}(876,\cdot)\) \(\chi_{3311}(981,\cdot)\) \(\chi_{3311}(1030,\cdot)\) \(\chi_{3311}(1086,\cdot)\) \(\chi_{3311}(1282,\cdot)\) \(\chi_{3311}(1569,\cdot)\) \(\chi_{3311}(1779,\cdot)\) \(\chi_{3311}(1933,\cdot)\) \(\chi_{3311}(1982,\cdot)\) \(\chi_{3311}(2185,\cdot)\) \(\chi_{3311}(2283,\cdot)\) \(\chi_{3311}(2290,\cdot)\) \(\chi_{3311}(2472,\cdot)\) \(\chi_{3311}(2591,\cdot)\) \(\chi_{3311}(2983,\cdot)\) \(\chi_{3311}(3088,\cdot)\) \(\chi_{3311}(3137,\cdot)\) \(\chi_{3311}(3186,\cdot)\) \(\chi_{3311}(3284,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1893,904,2927)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(127, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{33}{70}\right)\) |