Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1337}(614,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bu
\(\chi_{4011}(31,\cdot)\) \(\chi_{4011}(166,\cdot)\) \(\chi_{4011}(229,\cdot)\) \(\chi_{4011}(313,\cdot)\) \(\chi_{4011}(346,\cdot)\) \(\chi_{4011}(376,\cdot)\) \(\chi_{4011}(628,\cdot)\) \(\chi_{4011}(712,\cdot)\) \(\chi_{4011}(775,\cdot)\) \(\chi_{4011}(1039,\cdot)\) \(\chi_{4011}(1216,\cdot)\) \(\chi_{4011}(1312,\cdot)\) \(\chi_{4011}(1375,\cdot)\) \(\chi_{4011}(1459,\cdot)\) \(\chi_{4011}(1522,\cdot)\) \(\chi_{4011}(1594,\cdot)\) \(\chi_{4011}(1774,\cdot)\) \(\chi_{4011}(1858,\cdot)\) \(\chi_{4011}(1921,\cdot)\) \(\chi_{4011}(1951,\cdot)\) \(\chi_{4011}(2287,\cdot)\) \(\chi_{4011}(2329,\cdot)\) \(\chi_{4011}(2362,\cdot)\) \(\chi_{4011}(2497,\cdot)\) \(\chi_{4011}(2644,\cdot)\) \(\chi_{4011}(2740,\cdot)\) \(\chi_{4011}(2833,\cdot)\) \(\chi_{4011}(2896,\cdot)\) \(\chi_{4011}(3097,\cdot)\) \(\chi_{4011}(3211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{33}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(1951, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{2}{57}\right)\) |