Basic properties
Modulus: | \(4851\) | |
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: | no, induced from \(\chi_{1617}(26,\cdot)\) | 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)
|
Galois orbit 4851.fr
\(\chi_{4851}(26,\cdot)\) \(\chi_{4851}(152,\cdot)\) \(\chi_{4851}(269,\cdot)\) \(\chi_{4851}(278,\cdot)\) \(\chi_{4851}(467,\cdot)\) \(\chi_{4851}(647,\cdot)\) \(\chi_{4851}(719,\cdot)\) \(\chi_{4851}(773,\cdot)\) \(\chi_{4851}(845,\cdot)\) \(\chi_{4851}(971,\cdot)\) \(\chi_{4851}(1160,\cdot)\) \(\chi_{4851}(1214,\cdot)\) \(\chi_{4851}(1340,\cdot)\) \(\chi_{4851}(1412,\cdot)\) \(\chi_{4851}(1466,\cdot)\) \(\chi_{4851}(1655,\cdot)\) \(\chi_{4851}(1664,\cdot)\) \(\chi_{4851}(1853,\cdot)\) \(\chi_{4851}(1907,\cdot)\) \(\chi_{4851}(2033,\cdot)\) \(\chi_{4851}(2105,\cdot)\) \(\chi_{4851}(2159,\cdot)\) \(\chi_{4851}(2231,\cdot)\) \(\chi_{4851}(2348,\cdot)\) \(\chi_{4851}(2357,\cdot)\) \(\chi_{4851}(2546,\cdot)\) \(\chi_{4851}(2600,\cdot)\) \(\chi_{4851}(2798,\cdot)\) \(\chi_{4851}(2852,\cdot)\) \(\chi_{4851}(2924,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((-1,e\left(\frac{17}{42}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 4851 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{35}\right)\) |