Basic properties
| Modulus: | \(4027\) | |
| Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(671\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4027.m
\(\chi_{4027}(4,\cdot)\) \(\chi_{4027}(15,\cdot)\) \(\chi_{4027}(16,\cdot)\) \(\chi_{4027}(33,\cdot)\) \(\chi_{4027}(43,\cdot)\) \(\chi_{4027}(49,\cdot)\) \(\chi_{4027}(52,\cdot)\) \(\chi_{4027}(54,\cdot)\) \(\chi_{4027}(56,\cdot)\) \(\chi_{4027}(60,\cdot)\) \(\chi_{4027}(61,\cdot)\) \(\chi_{4027}(64,\cdot)\) \(\chi_{4027}(69,\cdot)\) \(\chi_{4027}(73,\cdot)\) \(\chi_{4027}(93,\cdot)\) \(\chi_{4027}(94,\cdot)\) \(\chi_{4027}(111,\cdot)\) \(\chi_{4027}(113,\cdot)\) \(\chi_{4027}(114,\cdot)\) \(\chi_{4027}(132,\cdot)\) \(\chi_{4027}(149,\cdot)\) \(\chi_{4027}(170,\cdot)\) \(\chi_{4027}(172,\cdot)\) \(\chi_{4027}(177,\cdot)\) \(\chi_{4027}(182,\cdot)\) \(\chi_{4027}(189,\cdot)\) \(\chi_{4027}(195,\cdot)\) \(\chi_{4027}(208,\cdot)\) \(\chi_{4027}(216,\cdot)\) \(\chi_{4027}(225,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{671})$ |
| Fixed field: | Number field defined by a degree 671 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{125}{671}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4027 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{576}{671}\right)\) | \(e\left(\frac{125}{671}\right)\) | \(e\left(\frac{481}{671}\right)\) | \(e\left(\frac{507}{671}\right)\) | \(e\left(\frac{30}{671}\right)\) | \(e\left(\frac{156}{671}\right)\) | \(e\left(\frac{386}{671}\right)\) | \(e\left(\frac{250}{671}\right)\) | \(e\left(\frac{412}{671}\right)\) | \(e\left(\frac{584}{671}\right)\) |