Basic properties
Modulus: | \(1723\) | |
Conductor: | \(1723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1722\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\(3\) → \(e\left(\frac{415}{1722}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1723 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{509}{574}\right)\) | \(e\left(\frac{415}{1722}\right)\) | \(e\left(\frac{222}{287}\right)\) | \(e\left(\frac{25}{574}\right)\) | \(e\left(\frac{110}{861}\right)\) | \(e\left(\frac{405}{574}\right)\) | \(e\left(\frac{379}{574}\right)\) | \(e\left(\frac{415}{861}\right)\) | \(e\left(\frac{267}{287}\right)\) | \(e\left(\frac{11}{21}\right)\) |