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.cz
\(\chi_{4017}(212,\cdot)\) \(\chi_{4017}(218,\cdot)\) \(\chi_{4017}(257,\cdot)\) \(\chi_{4017}(290,\cdot)\) \(\chi_{4017}(329,\cdot)\) \(\chi_{4017}(374,\cdot)\) \(\chi_{4017}(452,\cdot)\) \(\chi_{4017}(563,\cdot)\) \(\chi_{4017}(602,\cdot)\) \(\chi_{4017}(680,\cdot)\) \(\chi_{4017}(719,\cdot)\) \(\chi_{4017}(920,\cdot)\) \(\chi_{4017}(998,\cdot)\) \(\chi_{4017}(1154,\cdot)\) \(\chi_{4017}(1187,\cdot)\) \(\chi_{4017}(1232,\cdot)\) \(\chi_{4017}(1382,\cdot)\) \(\chi_{4017}(1427,\cdot)\) \(\chi_{4017}(1733,\cdot)\) \(\chi_{4017}(1889,\cdot)\) \(\chi_{4017}(1928,\cdot)\) \(\chi_{4017}(2168,\cdot)\) \(\chi_{4017}(2240,\cdot)\) \(\chi_{4017}(2558,\cdot)\) \(\chi_{4017}(2792,\cdot)\) \(\chi_{4017}(2825,\cdot)\) \(\chi_{4017}(3143,\cdot)\) \(\chi_{4017}(3260,\cdot)\) \(\chi_{4017}(3371,\cdot)\) \(\chi_{4017}(3572,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{83}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(212, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) |