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 \(\chi_{2415}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4830.dq
\(\chi_{4830}(53,\cdot)\) \(\chi_{4830}(107,\cdot)\) \(\chi_{4830}(263,\cdot)\) \(\chi_{4830}(527,\cdot)\) \(\chi_{4830}(557,\cdot)\) \(\chi_{4830}(893,\cdot)\) \(\chi_{4830}(977,\cdot)\) \(\chi_{4830}(1073,\cdot)\) \(\chi_{4830}(1157,\cdot)\) \(\chi_{4830}(1187,\cdot)\) \(\chi_{4830}(1367,\cdot)\) \(\chi_{4830}(1397,\cdot)\) \(\chi_{4830}(1493,\cdot)\) \(\chi_{4830}(1523,\cdot)\) \(\chi_{4830}(1607,\cdot)\) \(\chi_{4830}(1943,\cdot)\) \(\chi_{4830}(1997,\cdot)\) \(\chi_{4830}(2123,\cdot)\) \(\chi_{4830}(2153,\cdot)\) \(\chi_{4830}(2333,\cdot)\) \(\chi_{4830}(2363,\cdot)\) \(\chi_{4830}(2573,\cdot)\) \(\chi_{4830}(2627,\cdot)\) \(\chi_{4830}(2867,\cdot)\) \(\chi_{4830}(2963,\cdot)\) \(\chi_{4830}(3047,\cdot)\) \(\chi_{4830}(3257,\cdot)\) \(\chi_{4830}(3287,\cdot)\) \(\chi_{4830}(3467,\cdot)\) \(\chi_{4830}(3593,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3221,967,2761,1891)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 4830 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{5}{12}\right)\) |