Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(4067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1722\) | 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 4067.be
\(\chi_{4067}(2,\cdot)\) \(\chi_{4067}(32,\cdot)\) \(\chi_{4067}(39,\cdot)\) \(\chi_{4067}(46,\cdot)\) \(\chi_{4067}(53,\cdot)\) \(\chi_{4067}(58,\cdot)\) \(\chi_{4067}(60,\cdot)\) \(\chi_{4067}(72,\cdot)\) \(\chi_{4067}(74,\cdot)\) \(\chi_{4067}(88,\cdot)\) \(\chi_{4067}(102,\cdot)\) \(\chi_{4067}(107,\cdot)\) \(\chi_{4067}(130,\cdot)\) \(\chi_{4067}(135,\cdot)\) \(\chi_{4067}(137,\cdot)\) \(\chi_{4067}(149,\cdot)\) \(\chi_{4067}(156,\cdot)\) \(\chi_{4067}(163,\cdot)\) \(\chi_{4067}(172,\cdot)\) \(\chi_{4067}(179,\cdot)\) \(\chi_{4067}(184,\cdot)\) \(\chi_{4067}(186,\cdot)\) \(\chi_{4067}(198,\cdot)\) \(\chi_{4067}(200,\cdot)\) \(\chi_{4067}(205,\cdot)\) \(\chi_{4067}(212,\cdot)\) \(\chi_{4067}(219,\cdot)\) \(\chi_{4067}(221,\cdot)\) \(\chi_{4067}(228,\cdot)\) \(\chi_{4067}(233,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 1722 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{2}{21}\right),e\left(\frac{5}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{925}{1722}\right)\) | \(e\left(\frac{418}{861}\right)\) | \(e\left(\frac{64}{861}\right)\) | \(e\left(\frac{703}{1722}\right)\) | \(e\left(\frac{13}{574}\right)\) | \(e\left(\frac{351}{574}\right)\) | \(e\left(\frac{836}{861}\right)\) | \(e\left(\frac{814}{861}\right)\) | \(e\left(\frac{235}{861}\right)\) | \(e\left(\frac{482}{861}\right)\) |