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 \(\chi_{1339}(1294,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.ec
\(\chi_{4017}(7,\cdot)\) \(\chi_{4017}(28,\cdot)\) \(\chi_{4017}(58,\cdot)\) \(\chi_{4017}(136,\cdot)\) \(\chi_{4017}(232,\cdot)\) \(\chi_{4017}(448,\cdot)\) \(\chi_{4017}(475,\cdot)\) \(\chi_{4017}(544,\cdot)\) \(\chi_{4017}(553,\cdot)\) \(\chi_{4017}(565,\cdot)\) \(\chi_{4017}(574,\cdot)\) \(\chi_{4017}(583,\cdot)\) \(\chi_{4017}(670,\cdot)\) \(\chi_{4017}(709,\cdot)\) \(\chi_{4017}(739,\cdot)\) \(\chi_{4017}(916,\cdot)\) \(\chi_{4017}(1090,\cdot)\) \(\chi_{4017}(1150,\cdot)\) \(\chi_{4017}(1159,\cdot)\) \(\chi_{4017}(1285,\cdot)\) \(\chi_{4017}(1294,\cdot)\) \(\chi_{4017}(1372,\cdot)\) \(\chi_{4017}(1471,\cdot)\) \(\chi_{4017}(1510,\cdot)\) \(\chi_{4017}(1540,\cdot)\) \(\chi_{4017}(1666,\cdot)\) \(\chi_{4017}(1684,\cdot)\) \(\chi_{4017}(1753,\cdot)\) \(\chi_{4017}(1792,\cdot)\) \(\chi_{4017}(1801,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{14}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(1294, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{204}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{107}{204}\right)\) | \(e\left(\frac{37}{204}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{5}{102}\right)\) |