Basic properties
| Modulus: | \(3021\) | |
| Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 3021.cf
\(\chi_{3021}(8,\cdot)\) \(\chi_{3021}(50,\cdot)\) \(\chi_{3021}(65,\cdot)\) \(\chi_{3021}(164,\cdot)\) \(\chi_{3021}(179,\cdot)\) \(\chi_{3021}(350,\cdot)\) \(\chi_{3021}(392,\cdot)\) \(\chi_{3021}(563,\cdot)\) \(\chi_{3021}(578,\cdot)\) \(\chi_{3021}(677,\cdot)\) \(\chi_{3021}(692,\cdot)\) \(\chi_{3021}(734,\cdot)\) \(\chi_{3021}(920,\cdot)\) \(\chi_{3021}(962,\cdot)\) \(\chi_{3021}(1019,\cdot)\) \(\chi_{3021}(1034,\cdot)\) \(\chi_{3021}(1091,\cdot)\) \(\chi_{3021}(1133,\cdot)\) \(\chi_{3021}(1148,\cdot)\) \(\chi_{3021}(1205,\cdot)\) \(\chi_{3021}(1304,\cdot)\) \(\chi_{3021}(1376,\cdot)\) \(\chi_{3021}(1433,\cdot)\) \(\chi_{3021}(1532,\cdot)\) \(\chi_{3021}(1604,\cdot)\) \(\chi_{3021}(1646,\cdot)\) \(\chi_{3021}(1661,\cdot)\) \(\chi_{3021}(1718,\cdot)\) \(\chi_{3021}(1775,\cdot)\) \(\chi_{3021}(1874,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2015,1750,2281)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{31}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3021 }(2459, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{2}{39}\right)\) |