Basic properties
| Modulus: | \(4027\) | |
| Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4026\) | 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 4027.p
\(\chi_{4027}(3,\cdot)\) \(\chi_{4027}(5,\cdot)\) \(\chi_{4027}(11,\cdot)\) \(\chi_{4027}(12,\cdot)\) \(\chi_{4027}(18,\cdot)\) \(\chi_{4027}(20,\cdot)\) \(\chi_{4027}(31,\cdot)\) \(\chi_{4027}(34,\cdot)\) \(\chi_{4027}(37,\cdot)\) \(\chi_{4027}(38,\cdot)\) \(\chi_{4027}(39,\cdot)\) \(\chi_{4027}(42,\cdot)\) \(\chi_{4027}(44,\cdot)\) \(\chi_{4027}(45,\cdot)\) \(\chi_{4027}(48,\cdot)\) \(\chi_{4027}(50,\cdot)\) \(\chi_{4027}(51,\cdot)\) \(\chi_{4027}(58,\cdot)\) \(\chi_{4027}(59,\cdot)\) \(\chi_{4027}(63,\cdot)\) \(\chi_{4027}(65,\cdot)\) \(\chi_{4027}(70,\cdot)\) \(\chi_{4027}(72,\cdot)\) \(\chi_{4027}(75,\cdot)\) \(\chi_{4027}(80,\cdot)\) \(\chi_{4027}(82,\cdot)\) \(\chi_{4027}(87,\cdot)\) \(\chi_{4027}(92,\cdot)\) \(\chi_{4027}(95,\cdot)\) \(\chi_{4027}(99,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2013})$ |
| Fixed field: | Number field defined by a degree 4026 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{4026}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4027 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{125}{1342}\right)\) | \(e\left(\frac{1}{4026}\right)\) | \(e\left(\frac{125}{671}\right)\) | \(e\left(\frac{47}{4026}\right)\) | \(e\left(\frac{188}{2013}\right)\) | \(e\left(\frac{607}{1342}\right)\) | \(e\left(\frac{375}{1342}\right)\) | \(e\left(\frac{1}{2013}\right)\) | \(e\left(\frac{211}{2013}\right)\) | \(e\left(\frac{3875}{4026}\right)\) |