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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 1792.cc
\(\chi_{1792}(3,\cdot)\) \(\chi_{1792}(19,\cdot)\) \(\chi_{1792}(59,\cdot)\) \(\chi_{1792}(75,\cdot)\) \(\chi_{1792}(115,\cdot)\) \(\chi_{1792}(131,\cdot)\) \(\chi_{1792}(171,\cdot)\) \(\chi_{1792}(187,\cdot)\) \(\chi_{1792}(227,\cdot)\) \(\chi_{1792}(243,\cdot)\) \(\chi_{1792}(283,\cdot)\) \(\chi_{1792}(299,\cdot)\) \(\chi_{1792}(339,\cdot)\) \(\chi_{1792}(355,\cdot)\) \(\chi_{1792}(395,\cdot)\) \(\chi_{1792}(411,\cdot)\) \(\chi_{1792}(451,\cdot)\) \(\chi_{1792}(467,\cdot)\) \(\chi_{1792}(507,\cdot)\) \(\chi_{1792}(523,\cdot)\) \(\chi_{1792}(563,\cdot)\) \(\chi_{1792}(579,\cdot)\) \(\chi_{1792}(619,\cdot)\) \(\chi_{1792}(635,\cdot)\) \(\chi_{1792}(675,\cdot)\) \(\chi_{1792}(691,\cdot)\) \(\chi_{1792}(731,\cdot)\) \(\chi_{1792}(747,\cdot)\) \(\chi_{1792}(787,\cdot)\) \(\chi_{1792}(803,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{29}{64}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(171, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{192}\right)\) | \(e\left(\frac{55}{192}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{131}{192}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{145}{192}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{55}{96}\right)\) |