Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.dc
\(\chi_{4017}(113,\cdot)\) \(\chi_{4017}(230,\cdot)\) \(\chi_{4017}(542,\cdot)\) \(\chi_{4017}(698,\cdot)\) \(\chi_{4017}(731,\cdot)\) \(\chi_{4017}(815,\cdot)\) \(\chi_{4017}(848,\cdot)\) \(\chi_{4017}(893,\cdot)\) \(\chi_{4017}(1160,\cdot)\) \(\chi_{4017}(1316,\cdot)\) \(\chi_{4017}(1361,\cdot)\) \(\chi_{4017}(1433,\cdot)\) \(\chi_{4017}(1511,\cdot)\) \(\chi_{4017}(1634,\cdot)\) \(\chi_{4017}(1790,\cdot)\) \(\chi_{4017}(1979,\cdot)\) \(\chi_{4017}(2063,\cdot)\) \(\chi_{4017}(2102,\cdot)\) \(\chi_{4017}(2252,\cdot)\) \(\chi_{4017}(2258,\cdot)\) \(\chi_{4017}(2297,\cdot)\) \(\chi_{4017}(2408,\cdot)\) \(\chi_{4017}(2648,\cdot)\) \(\chi_{4017}(2681,\cdot)\) \(\chi_{4017}(2720,\cdot)\) \(\chi_{4017}(2876,\cdot)\) \(\chi_{4017}(2915,\cdot)\) \(\chi_{4017}(2921,\cdot)\) \(\chi_{4017}(3077,\cdot)\) \(\chi_{4017}(3266,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{15}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{73}{102}\right)\) |