Basic properties
| Modulus: | \(4600\) | |
| Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2300}(111,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4600.cy
\(\chi_{4600}(111,\cdot)\) \(\chi_{4600}(191,\cdot)\) \(\chi_{4600}(431,\cdot)\) \(\chi_{4600}(471,\cdot)\) \(\chi_{4600}(511,\cdot)\) \(\chi_{4600}(631,\cdot)\) \(\chi_{4600}(711,\cdot)\) \(\chi_{4600}(871,\cdot)\) \(\chi_{4600}(911,\cdot)\) \(\chi_{4600}(1031,\cdot)\) \(\chi_{4600}(1111,\cdot)\) \(\chi_{4600}(1391,\cdot)\) \(\chi_{4600}(1431,\cdot)\) \(\chi_{4600}(1631,\cdot)\) \(\chi_{4600}(1671,\cdot)\) \(\chi_{4600}(1791,\cdot)\) \(\chi_{4600}(1831,\cdot)\) \(\chi_{4600}(2031,\cdot)\) \(\chi_{4600}(2271,\cdot)\) \(\chi_{4600}(2311,\cdot)\) \(\chi_{4600}(2471,\cdot)\) \(\chi_{4600}(2591,\cdot)\) \(\chi_{4600}(2711,\cdot)\) \(\chi_{4600}(2871,\cdot)\) \(\chi_{4600}(3191,\cdot)\) \(\chi_{4600}(3231,\cdot)\) \(\chi_{4600}(3271,\cdot)\) \(\chi_{4600}(3391,\cdot)\) \(\chi_{4600}(3471,\cdot)\) \(\chi_{4600}(3511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((-1,1,e\left(\frac{4}{5}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) |