Basic properties
Modulus: | \(4830\) | |
Conductor: | \(2415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2415}(653,\cdot)\) | 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 4830.dk
\(\chi_{4830}(233,\cdot)\) \(\chi_{4830}(317,\cdot)\) \(\chi_{4830}(347,\cdot)\) \(\chi_{4830}(443,\cdot)\) \(\chi_{4830}(473,\cdot)\) \(\chi_{4830}(653,\cdot)\) \(\chi_{4830}(683,\cdot)\) \(\chi_{4830}(767,\cdot)\) \(\chi_{4830}(863,\cdot)\) \(\chi_{4830}(947,\cdot)\) \(\chi_{4830}(1283,\cdot)\) \(\chi_{4830}(1313,\cdot)\) \(\chi_{4830}(1577,\cdot)\) \(\chi_{4830}(1733,\cdot)\) \(\chi_{4830}(1787,\cdot)\) \(\chi_{4830}(1913,\cdot)\) \(\chi_{4830}(2027,\cdot)\) \(\chi_{4830}(2237,\cdot)\) \(\chi_{4830}(2417,\cdot)\) \(\chi_{4830}(2447,\cdot)\) \(\chi_{4830}(2543,\cdot)\) \(\chi_{4830}(2657,\cdot)\) \(\chi_{4830}(2753,\cdot)\) \(\chi_{4830}(2837,\cdot)\) \(\chi_{4830}(2993,\cdot)\) \(\chi_{4830}(3077,\cdot)\) \(\chi_{4830}(3203,\cdot)\) \(\chi_{4830}(3383,\cdot)\) \(\chi_{4830}(3413,\cdot)\) \(\chi_{4830}(3623,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((-1,-i,e\left(\frac{1}{3}\right),e\left(\frac{5}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 4830 }(653, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{11}{12}\right)\) |