Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(811,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.cu
\(\chi_{4017}(31,\cdot)\) \(\chi_{4017}(73,\cdot)\) \(\chi_{4017}(346,\cdot)\) \(\chi_{4017}(382,\cdot)\) \(\chi_{4017}(502,\cdot)\) \(\chi_{4017}(655,\cdot)\) \(\chi_{4017}(811,\cdot)\) \(\chi_{4017}(1555,\cdot)\) \(\chi_{4017}(1672,\cdot)\) \(\chi_{4017}(1864,\cdot)\) \(\chi_{4017}(1981,\cdot)\) \(\chi_{4017}(1984,\cdot)\) \(\chi_{4017}(2140,\cdot)\) \(\chi_{4017}(2257,\cdot)\) \(\chi_{4017}(2293,\cdot)\) \(\chi_{4017}(2335,\cdot)\) \(\chi_{4017}(2449,\cdot)\) \(\chi_{4017}(2566,\cdot)\) \(\chi_{4017}(2644,\cdot)\) \(\chi_{4017}(2803,\cdot)\) \(\chi_{4017}(3076,\cdot)\) \(\chi_{4017}(3112,\cdot)\) \(\chi_{4017}(3232,\cdot)\) \(\chi_{4017}(3385,\cdot)\) \(\chi_{4017}(3505,\cdot)\) \(\chi_{4017}(3541,\cdot)\) \(\chi_{4017}(3544,\cdot)\) \(\chi_{4017}(3700,\cdot)\) \(\chi_{4017}(3739,\cdot)\) \(\chi_{4017}(3814,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((1340,1237,1756)\) → \((1,-i,e\left(\frac{7}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(811, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) |