Basic properties
| Modulus: | \(4830\) | |
| Conductor: | \(2415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2415}(332,\cdot)\) | 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
\((3221,967,2761,1891)\) → \((-1,i,e\left(\frac{1}{6}\right),e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 4830 }(2747, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{12}\right)\) |