Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{309}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.dk
\(\chi_{4017}(53,\cdot)\) \(\chi_{4017}(170,\cdot)\) \(\chi_{4017}(482,\cdot)\) \(\chi_{4017}(521,\cdot)\) \(\chi_{4017}(560,\cdot)\) \(\chi_{4017}(599,\cdot)\) \(\chi_{4017}(638,\cdot)\) \(\chi_{4017}(872,\cdot)\) \(\chi_{4017}(911,\cdot)\) \(\chi_{4017}(989,\cdot)\) \(\chi_{4017}(1028,\cdot)\) \(\chi_{4017}(1145,\cdot)\) \(\chi_{4017}(1184,\cdot)\) \(\chi_{4017}(1301,\cdot)\) \(\chi_{4017}(1379,\cdot)\) \(\chi_{4017}(1496,\cdot)\) \(\chi_{4017}(1691,\cdot)\) \(\chi_{4017}(1847,\cdot)\) \(\chi_{4017}(1925,\cdot)\) \(\chi_{4017}(2042,\cdot)\) \(\chi_{4017}(2081,\cdot)\) \(\chi_{4017}(2159,\cdot)\) \(\chi_{4017}(2198,\cdot)\) \(\chi_{4017}(2237,\cdot)\) \(\chi_{4017}(2354,\cdot)\) \(\chi_{4017}(2549,\cdot)\) \(\chi_{4017}(3095,\cdot)\) \(\chi_{4017}(3134,\cdot)\) \(\chi_{4017}(3485,\cdot)\) \(\chi_{4017}(3680,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,1,e\left(\frac{97}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) |