Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(334,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.cq
\(\chi_{4017}(334,\cdot)\) \(\chi_{4017}(367,\cdot)\) \(\chi_{4017}(445,\cdot)\) \(\chi_{4017}(646,\cdot)\) \(\chi_{4017}(757,\cdot)\) \(\chi_{4017}(874,\cdot)\) \(\chi_{4017}(1192,\cdot)\) \(\chi_{4017}(1225,\cdot)\) \(\chi_{4017}(1459,\cdot)\) \(\chi_{4017}(1777,\cdot)\) \(\chi_{4017}(1849,\cdot)\) \(\chi_{4017}(2089,\cdot)\) \(\chi_{4017}(2128,\cdot)\) \(\chi_{4017}(2284,\cdot)\) \(\chi_{4017}(2590,\cdot)\) \(\chi_{4017}(2635,\cdot)\) \(\chi_{4017}(2785,\cdot)\) \(\chi_{4017}(2830,\cdot)\) \(\chi_{4017}(2863,\cdot)\) \(\chi_{4017}(3019,\cdot)\) \(\chi_{4017}(3097,\cdot)\) \(\chi_{4017}(3298,\cdot)\) \(\chi_{4017}(3337,\cdot)\) \(\chi_{4017}(3415,\cdot)\) \(\chi_{4017}(3454,\cdot)\) \(\chi_{4017}(3565,\cdot)\) \(\chi_{4017}(3643,\cdot)\) \(\chi_{4017}(3688,\cdot)\) \(\chi_{4017}(3727,\cdot)\) \(\chi_{4017}(3760,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{1}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(334, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) |