Basic properties
Modulus: | \(4830\) | |
Conductor: | \(2415\) | 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 \(\chi_{2415}(962,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4830.do
\(\chi_{4830}(17,\cdot)\) \(\chi_{4830}(143,\cdot)\) \(\chi_{4830}(227,\cdot)\) \(\chi_{4830}(383,\cdot)\) \(\chi_{4830}(467,\cdot)\) \(\chi_{4830}(563,\cdot)\) \(\chi_{4830}(677,\cdot)\) \(\chi_{4830}(773,\cdot)\) \(\chi_{4830}(803,\cdot)\) \(\chi_{4830}(983,\cdot)\) \(\chi_{4830}(1193,\cdot)\) \(\chi_{4830}(1307,\cdot)\) \(\chi_{4830}(1433,\cdot)\) \(\chi_{4830}(1487,\cdot)\) \(\chi_{4830}(1643,\cdot)\) \(\chi_{4830}(1907,\cdot)\) \(\chi_{4830}(1937,\cdot)\) \(\chi_{4830}(2273,\cdot)\) \(\chi_{4830}(2357,\cdot)\) \(\chi_{4830}(2453,\cdot)\) \(\chi_{4830}(2537,\cdot)\) \(\chi_{4830}(2567,\cdot)\) \(\chi_{4830}(2747,\cdot)\) \(\chi_{4830}(2777,\cdot)\) \(\chi_{4830}(2873,\cdot)\) \(\chi_{4830}(2903,\cdot)\) \(\chi_{4830}(2987,\cdot)\) \(\chi_{4830}(3323,\cdot)\) \(\chi_{4830}(3377,\cdot)\) \(\chi_{4830}(3503,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((-1,i,e\left(\frac{1}{6}\right),e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 4830 }(3377, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{119}{132}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{12}\right)\) |