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.cb
\(\chi_{1792}(37,\cdot)\) \(\chi_{1792}(53,\cdot)\) \(\chi_{1792}(93,\cdot)\) \(\chi_{1792}(109,\cdot)\) \(\chi_{1792}(149,\cdot)\) \(\chi_{1792}(165,\cdot)\) \(\chi_{1792}(205,\cdot)\) \(\chi_{1792}(221,\cdot)\) \(\chi_{1792}(261,\cdot)\) \(\chi_{1792}(277,\cdot)\) \(\chi_{1792}(317,\cdot)\) \(\chi_{1792}(333,\cdot)\) \(\chi_{1792}(373,\cdot)\) \(\chi_{1792}(389,\cdot)\) \(\chi_{1792}(429,\cdot)\) \(\chi_{1792}(445,\cdot)\) \(\chi_{1792}(485,\cdot)\) \(\chi_{1792}(501,\cdot)\) \(\chi_{1792}(541,\cdot)\) \(\chi_{1792}(557,\cdot)\) \(\chi_{1792}(597,\cdot)\) \(\chi_{1792}(613,\cdot)\) \(\chi_{1792}(653,\cdot)\) \(\chi_{1792}(669,\cdot)\) \(\chi_{1792}(709,\cdot)\) \(\chi_{1792}(725,\cdot)\) \(\chi_{1792}(765,\cdot)\) \(\chi_{1792}(781,\cdot)\) \(\chi_{1792}(821,\cdot)\) \(\chi_{1792}(837,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{9}{64}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(613, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{192}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{119}{192}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{109}{192}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{91}{96}\right)\) |