Basic properties
| Modulus: | \(1723\) | |
| Conductor: | \(1723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(861\) | 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 1723.o
\(\chi_{1723}(6,\cdot)\) \(\chi_{1723}(9,\cdot)\) \(\chi_{1723}(19,\cdot)\) \(\chi_{1723}(21,\cdot)\) \(\chi_{1723}(23,\cdot)\) \(\chi_{1723}(24,\cdot)\) \(\chi_{1723}(34,\cdot)\) \(\chi_{1723}(36,\cdot)\) \(\chi_{1723}(37,\cdot)\) \(\chi_{1723}(39,\cdot)\) \(\chi_{1723}(43,\cdot)\) \(\chi_{1723}(44,\cdot)\) \(\chi_{1723}(47,\cdot)\) \(\chi_{1723}(58,\cdot)\) \(\chi_{1723}(60,\cdot)\) \(\chi_{1723}(61,\cdot)\) \(\chi_{1723}(67,\cdot)\) \(\chi_{1723}(81,\cdot)\) \(\chi_{1723}(84,\cdot)\) \(\chi_{1723}(85,\cdot)\) \(\chi_{1723}(90,\cdot)\) \(\chi_{1723}(92,\cdot)\) \(\chi_{1723}(93,\cdot)\) \(\chi_{1723}(99,\cdot)\) \(\chi_{1723}(101,\cdot)\) \(\chi_{1723}(103,\cdot)\) \(\chi_{1723}(109,\cdot)\) \(\chi_{1723}(110,\cdot)\) \(\chi_{1723}(113,\cdot)\) \(\chi_{1723}(114,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 861 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{580}{861}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1723 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{287}\right)\) | \(e\left(\frac{580}{861}\right)\) | \(e\left(\frac{254}{287}\right)\) | \(e\left(\frac{194}{287}\right)\) | \(e\left(\frac{100}{861}\right)\) | \(e\left(\frac{158}{287}\right)\) | \(e\left(\frac{94}{287}\right)\) | \(e\left(\frac{299}{861}\right)\) | \(e\left(\frac{34}{287}\right)\) | \(e\left(\frac{10}{21}\right)\) |