Basic properties
| Modulus: | \(1723\) | |
| Conductor: | \(1723\) | 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 1723.p
\(\chi_{1723}(3,\cdot)\) \(\chi_{1723}(12,\cdot)\) \(\chi_{1723}(17,\cdot)\) \(\chi_{1723}(18,\cdot)\) \(\chi_{1723}(29,\cdot)\) \(\chi_{1723}(30,\cdot)\) \(\chi_{1723}(38,\cdot)\) \(\chi_{1723}(45,\cdot)\) \(\chi_{1723}(46,\cdot)\) \(\chi_{1723}(48,\cdot)\) \(\chi_{1723}(55,\cdot)\) \(\chi_{1723}(63,\cdot)\) \(\chi_{1723}(74,\cdot)\) \(\chi_{1723}(75,\cdot)\) \(\chi_{1723}(77,\cdot)\) \(\chi_{1723}(78,\cdot)\) \(\chi_{1723}(82,\cdot)\) \(\chi_{1723}(83,\cdot)\) \(\chi_{1723}(86,\cdot)\) \(\chi_{1723}(88,\cdot)\) \(\chi_{1723}(94,\cdot)\) \(\chi_{1723}(95,\cdot)\) \(\chi_{1723}(105,\cdot)\) \(\chi_{1723}(107,\cdot)\) \(\chi_{1723}(115,\cdot)\) \(\chi_{1723}(116,\cdot)\) \(\chi_{1723}(117,\cdot)\) \(\chi_{1723}(120,\cdot)\) \(\chi_{1723}(122,\cdot)\) \(\chi_{1723}(127,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 1722 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{209}{1722}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1723 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{574}\right)\) | \(e\left(\frac{209}{1722}\right)\) | \(e\left(\frac{71}{287}\right)\) | \(e\left(\frac{61}{574}\right)\) | \(e\left(\frac{211}{861}\right)\) | \(e\left(\frac{529}{574}\right)\) | \(e\left(\frac{213}{574}\right)\) | \(e\left(\frac{209}{861}\right)\) | \(e\left(\frac{66}{287}\right)\) | \(e\left(\frac{19}{21}\right)\) |