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 \(\chi_{1339}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.cw
\(\chi_{4017}(34,\cdot)\) \(\chi_{4017}(112,\cdot)\) \(\chi_{4017}(229,\cdot)\) \(\chi_{4017}(343,\cdot)\) \(\chi_{4017}(385,\cdot)\) \(\chi_{4017}(421,\cdot)\) \(\chi_{4017}(538,\cdot)\) \(\chi_{4017}(694,\cdot)\) \(\chi_{4017}(697,\cdot)\) \(\chi_{4017}(814,\cdot)\) \(\chi_{4017}(1006,\cdot)\) \(\chi_{4017}(1123,\cdot)\) \(\chi_{4017}(1867,\cdot)\) \(\chi_{4017}(2023,\cdot)\) \(\chi_{4017}(2176,\cdot)\) \(\chi_{4017}(2296,\cdot)\) \(\chi_{4017}(2332,\cdot)\) \(\chi_{4017}(2605,\cdot)\) \(\chi_{4017}(2647,\cdot)\) \(\chi_{4017}(2686,\cdot)\) \(\chi_{4017}(2842,\cdot)\) \(\chi_{4017}(2881,\cdot)\) \(\chi_{4017}(2956,\cdot)\) \(\chi_{4017}(2995,\cdot)\) \(\chi_{4017}(3151,\cdot)\) \(\chi_{4017}(3154,\cdot)\) \(\chi_{4017}(3190,\cdot)\) \(\chi_{4017}(3310,\cdot)\) \(\chi_{4017}(3463,\cdot)\) \(\chi_{4017}(3583,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((1340,1237,1756)\) → \((1,i,e\left(\frac{2}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) |