Basic properties
| Modulus: | \(4840\) | |
| Conductor: | \(4840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4840.dn
\(\chi_{4840}(147,\cdot)\) \(\chi_{4840}(163,\cdot)\) \(\chi_{4840}(203,\cdot)\) \(\chi_{4840}(267,\cdot)\) \(\chi_{4840}(427,\cdot)\) \(\chi_{4840}(443,\cdot)\) \(\chi_{4840}(467,\cdot)\) \(\chi_{4840}(587,\cdot)\) \(\chi_{4840}(603,\cdot)\) \(\chi_{4840}(643,\cdot)\) \(\chi_{4840}(707,\cdot)\) \(\chi_{4840}(763,\cdot)\) \(\chi_{4840}(867,\cdot)\) \(\chi_{4840}(883,\cdot)\) \(\chi_{4840}(907,\cdot)\) \(\chi_{4840}(1027,\cdot)\) \(\chi_{4840}(1043,\cdot)\) \(\chi_{4840}(1083,\cdot)\) \(\chi_{4840}(1147,\cdot)\) \(\chi_{4840}(1203,\cdot)\) \(\chi_{4840}(1307,\cdot)\) \(\chi_{4840}(1323,\cdot)\) \(\chi_{4840}(1347,\cdot)\) \(\chi_{4840}(1467,\cdot)\) \(\chi_{4840}(1483,\cdot)\) \(\chi_{4840}(1523,\cdot)\) \(\chi_{4840}(1587,\cdot)\) \(\chi_{4840}(1643,\cdot)\) \(\chi_{4840}(1747,\cdot)\) \(\chi_{4840}(1763,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-1,-i,e\left(\frac{8}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4840 }(1043, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{59}{220}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{26}{55}\right)\) |