Basic properties
Modulus: | \(1617\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(210\) | 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)
|
Galois orbit 1617.cl
\(\chi_{1617}(53,\cdot)\) \(\chi_{1617}(86,\cdot)\) \(\chi_{1617}(137,\cdot)\) \(\chi_{1617}(158,\cdot)\) \(\chi_{1617}(170,\cdot)\) \(\chi_{1617}(179,\cdot)\) \(\chi_{1617}(191,\cdot)\) \(\chi_{1617}(212,\cdot)\) \(\chi_{1617}(284,\cdot)\) \(\chi_{1617}(317,\cdot)\) \(\chi_{1617}(368,\cdot)\) \(\chi_{1617}(389,\cdot)\) \(\chi_{1617}(401,\cdot)\) \(\chi_{1617}(443,\cdot)\) \(\chi_{1617}(515,\cdot)\) \(\chi_{1617}(548,\cdot)\) \(\chi_{1617}(599,\cdot)\) \(\chi_{1617}(620,\cdot)\) \(\chi_{1617}(632,\cdot)\) \(\chi_{1617}(641,\cdot)\) \(\chi_{1617}(653,\cdot)\) \(\chi_{1617}(674,\cdot)\) \(\chi_{1617}(746,\cdot)\) \(\chi_{1617}(779,\cdot)\) \(\chi_{1617}(830,\cdot)\) \(\chi_{1617}(872,\cdot)\) \(\chi_{1617}(884,\cdot)\) \(\chi_{1617}(905,\cdot)\) \(\chi_{1617}(977,\cdot)\) \(\chi_{1617}(1061,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{5}{21}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{27}{70}\right)\) |