Basic properties
| Modulus: | \(4830\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{805}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4830.dl
\(\chi_{4830}(103,\cdot)\) \(\chi_{4830}(157,\cdot)\) \(\chi_{4830}(283,\cdot)\) \(\chi_{4830}(313,\cdot)\) \(\chi_{4830}(493,\cdot)\) \(\chi_{4830}(523,\cdot)\) \(\chi_{4830}(733,\cdot)\) \(\chi_{4830}(787,\cdot)\) \(\chi_{4830}(1027,\cdot)\) \(\chi_{4830}(1123,\cdot)\) \(\chi_{4830}(1207,\cdot)\) \(\chi_{4830}(1417,\cdot)\) \(\chi_{4830}(1447,\cdot)\) \(\chi_{4830}(1627,\cdot)\) \(\chi_{4830}(1753,\cdot)\) \(\chi_{4830}(1837,\cdot)\) \(\chi_{4830}(1993,\cdot)\) \(\chi_{4830}(2077,\cdot)\) \(\chi_{4830}(2173,\cdot)\) \(\chi_{4830}(2287,\cdot)\) \(\chi_{4830}(2383,\cdot)\) \(\chi_{4830}(2413,\cdot)\) \(\chi_{4830}(2593,\cdot)\) \(\chi_{4830}(2803,\cdot)\) \(\chi_{4830}(2917,\cdot)\) \(\chi_{4830}(3043,\cdot)\) \(\chi_{4830}(3097,\cdot)\) \(\chi_{4830}(3253,\cdot)\) \(\chi_{4830}(3517,\cdot)\) \(\chi_{4830}(3547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((1,-i,e\left(\frac{5}{6}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 4830 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{11}{12}\right)\) |