Basic properties
Modulus: | \(1792\) | |
Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(192\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 1792.cd
\(\chi_{1792}(11,\cdot)\) \(\chi_{1792}(51,\cdot)\) \(\chi_{1792}(67,\cdot)\) \(\chi_{1792}(107,\cdot)\) \(\chi_{1792}(123,\cdot)\) \(\chi_{1792}(163,\cdot)\) \(\chi_{1792}(179,\cdot)\) \(\chi_{1792}(219,\cdot)\) \(\chi_{1792}(235,\cdot)\) \(\chi_{1792}(275,\cdot)\) \(\chi_{1792}(291,\cdot)\) \(\chi_{1792}(331,\cdot)\) \(\chi_{1792}(347,\cdot)\) \(\chi_{1792}(387,\cdot)\) \(\chi_{1792}(403,\cdot)\) \(\chi_{1792}(443,\cdot)\) \(\chi_{1792}(459,\cdot)\) \(\chi_{1792}(499,\cdot)\) \(\chi_{1792}(515,\cdot)\) \(\chi_{1792}(555,\cdot)\) \(\chi_{1792}(571,\cdot)\) \(\chi_{1792}(611,\cdot)\) \(\chi_{1792}(627,\cdot)\) \(\chi_{1792}(667,\cdot)\) \(\chi_{1792}(683,\cdot)\) \(\chi_{1792}(723,\cdot)\) \(\chi_{1792}(739,\cdot)\) \(\chi_{1792}(779,\cdot)\) \(\chi_{1792}(795,\cdot)\) \(\chi_{1792}(835,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{33}{64}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(123, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{192}\right)\) | \(e\left(\frac{163}{192}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{191}{192}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{133}{192}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{67}{96}\right)\) |