Basic properties
| Modulus: | \(4600\) | |
| Conductor: | \(4600\) | 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 4600.dp
\(\chi_{4600}(3,\cdot)\) \(\chi_{4600}(27,\cdot)\) \(\chi_{4600}(123,\cdot)\) \(\chi_{4600}(147,\cdot)\) \(\chi_{4600}(163,\cdot)\) \(\chi_{4600}(187,\cdot)\) \(\chi_{4600}(347,\cdot)\) \(\chi_{4600}(363,\cdot)\) \(\chi_{4600}(403,\cdot)\) \(\chi_{4600}(427,\cdot)\) \(\chi_{4600}(547,\cdot)\) \(\chi_{4600}(587,\cdot)\) \(\chi_{4600}(627,\cdot)\) \(\chi_{4600}(683,\cdot)\) \(\chi_{4600}(763,\cdot)\) \(\chi_{4600}(867,\cdot)\) \(\chi_{4600}(883,\cdot)\) \(\chi_{4600}(923,\cdot)\) \(\chi_{4600}(947,\cdot)\) \(\chi_{4600}(1067,\cdot)\) \(\chi_{4600}(1083,\cdot)\) \(\chi_{4600}(1163,\cdot)\) \(\chi_{4600}(1227,\cdot)\) \(\chi_{4600}(1267,\cdot)\) \(\chi_{4600}(1283,\cdot)\) \(\chi_{4600}(1323,\cdot)\) \(\chi_{4600}(1347,\cdot)\) \(\chi_{4600}(1363,\cdot)\) \(\chi_{4600}(1467,\cdot)\) \(\chi_{4600}(1547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((-1,-1,e\left(\frac{1}{20}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(1227, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{220}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{59}{220}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) |