Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bt
\(\chi_{4011}(38,\cdot)\) \(\chi_{4011}(122,\cdot)\) \(\chi_{4011}(185,\cdot)\) \(\chi_{4011}(257,\cdot)\) \(\chi_{4011}(437,\cdot)\) \(\chi_{4011}(521,\cdot)\) \(\chi_{4011}(584,\cdot)\) \(\chi_{4011}(614,\cdot)\) \(\chi_{4011}(950,\cdot)\) \(\chi_{4011}(992,\cdot)\) \(\chi_{4011}(1025,\cdot)\) \(\chi_{4011}(1160,\cdot)\) \(\chi_{4011}(1307,\cdot)\) \(\chi_{4011}(1403,\cdot)\) \(\chi_{4011}(1496,\cdot)\) \(\chi_{4011}(1559,\cdot)\) \(\chi_{4011}(1760,\cdot)\) \(\chi_{4011}(1874,\cdot)\) \(\chi_{4011}(2096,\cdot)\) \(\chi_{4011}(2138,\cdot)\) \(\chi_{4011}(2306,\cdot)\) \(\chi_{4011}(2453,\cdot)\) \(\chi_{4011}(2567,\cdot)\) \(\chi_{4011}(2642,\cdot)\) \(\chi_{4011}(2705,\cdot)\) \(\chi_{4011}(2840,\cdot)\) \(\chi_{4011}(2903,\cdot)\) \(\chi_{4011}(2987,\cdot)\) \(\chi_{4011}(3020,\cdot)\) \(\chi_{4011}(3050,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(1874, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) |