Basic properties
Modulus: | \(1723\) | |
Conductor: | \(1723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(574\) | 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.n
\(\chi_{1723}(2,\cdot)\) \(\chi_{1723}(5,\cdot)\) \(\chi_{1723}(7,\cdot)\) \(\chi_{1723}(8,\cdot)\) \(\chi_{1723}(13,\cdot)\) \(\chi_{1723}(27,\cdot)\) \(\chi_{1723}(28,\cdot)\) \(\chi_{1723}(31,\cdot)\) \(\chi_{1723}(32,\cdot)\) \(\chi_{1723}(33,\cdot)\) \(\chi_{1723}(50,\cdot)\) \(\chi_{1723}(52,\cdot)\) \(\chi_{1723}(53,\cdot)\) \(\chi_{1723}(59,\cdot)\) \(\chi_{1723}(69,\cdot)\) \(\chi_{1723}(70,\cdot)\) \(\chi_{1723}(73,\cdot)\) \(\chi_{1723}(80,\cdot)\) \(\chi_{1723}(97,\cdot)\) \(\chi_{1723}(98,\cdot)\) \(\chi_{1723}(102,\cdot)\) \(\chi_{1723}(108,\cdot)\) \(\chi_{1723}(111,\cdot)\) \(\chi_{1723}(112,\cdot)\) \(\chi_{1723}(123,\cdot)\) \(\chi_{1723}(124,\cdot)\) \(\chi_{1723}(125,\cdot)\) \(\chi_{1723}(131,\cdot)\) \(\chi_{1723}(132,\cdot)\) \(\chi_{1723}(173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{287})$ |
Fixed field: | Number field defined by a degree 574 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{313}{574}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1723 }(98, a) \) | \(-1\) | \(1\) | \(e\left(\frac{503}{574}\right)\) | \(e\left(\frac{313}{574}\right)\) | \(e\left(\frac{216}{287}\right)\) | \(e\left(\frac{513}{574}\right)\) | \(e\left(\frac{121}{287}\right)\) | \(e\left(\frac{45}{574}\right)\) | \(e\left(\frac{361}{574}\right)\) | \(e\left(\frac{26}{287}\right)\) | \(e\left(\frac{221}{287}\right)\) | \(e\left(\frac{3}{7}\right)\) |