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.dy
\(\chi_{4017}(35,\cdot)\) \(\chi_{4017}(74,\cdot)\) \(\chi_{4017}(302,\cdot)\) \(\chi_{4017}(380,\cdot)\) \(\chi_{4017}(386,\cdot)\) \(\chi_{4017}(536,\cdot)\) \(\chi_{4017}(614,\cdot)\) \(\chi_{4017}(809,\cdot)\) \(\chi_{4017}(971,\cdot)\) \(\chi_{4017}(1517,\cdot)\) \(\chi_{4017}(1550,\cdot)\) \(\chi_{4017}(1829,\cdot)\) \(\chi_{4017}(1940,\cdot)\) \(\chi_{4017}(2174,\cdot)\) \(\chi_{4017}(2375,\cdot)\) \(\chi_{4017}(2453,\cdot)\) \(\chi_{4017}(2492,\cdot)\) \(\chi_{4017}(2525,\cdot)\) \(\chi_{4017}(2642,\cdot)\) \(\chi_{4017}(2726,\cdot)\) \(\chi_{4017}(2765,\cdot)\) \(\chi_{4017}(2843,\cdot)\) \(\chi_{4017}(2882,\cdot)\) \(\chi_{4017}(2954,\cdot)\) \(\chi_{4017}(3032,\cdot)\) \(\chi_{4017}(3350,\cdot)\) \(\chi_{4017}(3545,\cdot)\) \(\chi_{4017}(3617,\cdot)\) \(\chi_{4017}(3656,\cdot)\) \(\chi_{4017}(3773,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(1550, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) |