Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.dz
\(\chi_{4017}(43,\cdot)\) \(\chi_{4017}(88,\cdot)\) \(\chi_{4017}(394,\cdot)\) \(\chi_{4017}(550,\cdot)\) \(\chi_{4017}(589,\cdot)\) \(\chi_{4017}(829,\cdot)\) \(\chi_{4017}(901,\cdot)\) \(\chi_{4017}(1219,\cdot)\) \(\chi_{4017}(1453,\cdot)\) \(\chi_{4017}(1486,\cdot)\) \(\chi_{4017}(1804,\cdot)\) \(\chi_{4017}(1921,\cdot)\) \(\chi_{4017}(2032,\cdot)\) \(\chi_{4017}(2233,\cdot)\) \(\chi_{4017}(2311,\cdot)\) \(\chi_{4017}(2344,\cdot)\) \(\chi_{4017}(2890,\cdot)\) \(\chi_{4017}(2896,\cdot)\) \(\chi_{4017}(2935,\cdot)\) \(\chi_{4017}(2968,\cdot)\) \(\chi_{4017}(3007,\cdot)\) \(\chi_{4017}(3052,\cdot)\) \(\chi_{4017}(3130,\cdot)\) \(\chi_{4017}(3241,\cdot)\) \(\chi_{4017}(3280,\cdot)\) \(\chi_{4017}(3358,\cdot)\) \(\chi_{4017}(3397,\cdot)\) \(\chi_{4017}(3598,\cdot)\) \(\chi_{4017}(3676,\cdot)\) \(\chi_{4017}(3832,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{77}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) |