Basic properties
Modulus: | \(4830\) | |
Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{805}(397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4830.dr
\(\chi_{4830}(73,\cdot)\) \(\chi_{4830}(187,\cdot)\) \(\chi_{4830}(397,\cdot)\) \(\chi_{4830}(577,\cdot)\) \(\chi_{4830}(607,\cdot)\) \(\chi_{4830}(703,\cdot)\) \(\chi_{4830}(817,\cdot)\) \(\chi_{4830}(913,\cdot)\) \(\chi_{4830}(997,\cdot)\) \(\chi_{4830}(1153,\cdot)\) \(\chi_{4830}(1237,\cdot)\) \(\chi_{4830}(1363,\cdot)\) \(\chi_{4830}(1543,\cdot)\) \(\chi_{4830}(1573,\cdot)\) \(\chi_{4830}(1783,\cdot)\) \(\chi_{4830}(1867,\cdot)\) \(\chi_{4830}(1963,\cdot)\) \(\chi_{4830}(2203,\cdot)\) \(\chi_{4830}(2257,\cdot)\) \(\chi_{4830}(2467,\cdot)\) \(\chi_{4830}(2497,\cdot)\) \(\chi_{4830}(2677,\cdot)\) \(\chi_{4830}(2707,\cdot)\) \(\chi_{4830}(2833,\cdot)\) \(\chi_{4830}(2887,\cdot)\) \(\chi_{4830}(3223,\cdot)\) \(\chi_{4830}(3307,\cdot)\) \(\chi_{4830}(3337,\cdot)\) \(\chi_{4830}(3433,\cdot)\) \(\chi_{4830}(3463,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((1,i,e\left(\frac{5}{6}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 4830 }(397, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{12}\right)\) |