Basic properties
Modulus: | \(4851\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4851.ez
\(\chi_{4851}(37,\cdot)\) \(\chi_{4851}(163,\cdot)\) \(\chi_{4851}(235,\cdot)\) \(\chi_{4851}(289,\cdot)\) \(\chi_{4851}(478,\cdot)\) \(\chi_{4851}(487,\cdot)\) \(\chi_{4851}(676,\cdot)\) \(\chi_{4851}(730,\cdot)\) \(\chi_{4851}(856,\cdot)\) \(\chi_{4851}(928,\cdot)\) \(\chi_{4851}(982,\cdot)\) \(\chi_{4851}(1054,\cdot)\) \(\chi_{4851}(1171,\cdot)\) \(\chi_{4851}(1180,\cdot)\) \(\chi_{4851}(1369,\cdot)\) \(\chi_{4851}(1423,\cdot)\) \(\chi_{4851}(1621,\cdot)\) \(\chi_{4851}(1675,\cdot)\) \(\chi_{4851}(1747,\cdot)\) \(\chi_{4851}(1864,\cdot)\) \(\chi_{4851}(1873,\cdot)\) \(\chi_{4851}(2062,\cdot)\) \(\chi_{4851}(2116,\cdot)\) \(\chi_{4851}(2242,\cdot)\) \(\chi_{4851}(2314,\cdot)\) \(\chi_{4851}(2368,\cdot)\) \(\chi_{4851}(2440,\cdot)\) \(\chi_{4851}(2557,\cdot)\) \(\chi_{4851}(2755,\cdot)\) \(\chi_{4851}(2809,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((1,e\left(\frac{16}{21}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 4851 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{32}{35}\right)\) |