Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.eh
\(\chi_{4017}(37,\cdot)\) \(\chi_{4017}(106,\cdot)\) \(\chi_{4017}(145,\cdot)\) \(\chi_{4017}(193,\cdot)\) \(\chi_{4017}(301,\cdot)\) \(\chi_{4017}(319,\cdot)\) \(\chi_{4017}(331,\cdot)\) \(\chi_{4017}(340,\cdot)\) \(\chi_{4017}(436,\cdot)\) \(\chi_{4017}(604,\cdot)\) \(\chi_{4017}(691,\cdot)\) \(\chi_{4017}(748,\cdot)\) \(\chi_{4017}(760,\cdot)\) \(\chi_{4017}(904,\cdot)\) \(\chi_{4017}(964,\cdot)\) \(\chi_{4017}(1021,\cdot)\) \(\chi_{4017}(1033,\cdot)\) \(\chi_{4017}(1072,\cdot)\) \(\chi_{4017}(1099,\cdot)\) \(\chi_{4017}(1120,\cdot)\) \(\chi_{4017}(1228,\cdot)\) \(\chi_{4017}(1246,\cdot)\) \(\chi_{4017}(1267,\cdot)\) \(\chi_{4017}(1363,\cdot)\) \(\chi_{4017}(1567,\cdot)\) \(\chi_{4017}(1618,\cdot)\) \(\chi_{4017}(1675,\cdot)\) \(\chi_{4017}(1831,\cdot)\) \(\chi_{4017}(1840,\cdot)\) \(\chi_{4017}(1891,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{7}{12}\right),e\left(\frac{31}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{204}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{143}{204}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{101}{102}\right)\) |