Basic properties
| Modulus: | \(2420\) | |
| Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{484}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2420.bp
\(\chi_{2420}(31,\cdot)\) \(\chi_{2420}(71,\cdot)\) \(\chi_{2420}(91,\cdot)\) \(\chi_{2420}(191,\cdot)\) \(\chi_{2420}(291,\cdot)\) \(\chi_{2420}(311,\cdot)\) \(\chi_{2420}(411,\cdot)\) \(\chi_{2420}(471,\cdot)\) \(\chi_{2420}(531,\cdot)\) \(\chi_{2420}(631,\cdot)\) \(\chi_{2420}(691,\cdot)\) \(\chi_{2420}(731,\cdot)\) \(\chi_{2420}(751,\cdot)\) \(\chi_{2420}(851,\cdot)\) \(\chi_{2420}(911,\cdot)\) \(\chi_{2420}(951,\cdot)\) \(\chi_{2420}(1071,\cdot)\) \(\chi_{2420}(1131,\cdot)\) \(\chi_{2420}(1171,\cdot)\) \(\chi_{2420}(1191,\cdot)\) \(\chi_{2420}(1351,\cdot)\) \(\chi_{2420}(1391,\cdot)\) \(\chi_{2420}(1411,\cdot)\) \(\chi_{2420}(1511,\cdot)\) \(\chi_{2420}(1571,\cdot)\) \(\chi_{2420}(1611,\cdot)\) \(\chi_{2420}(1631,\cdot)\) \(\chi_{2420}(1731,\cdot)\) \(\chi_{2420}(1791,\cdot)\) \(\chi_{2420}(1831,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,1937,2301)\) → \((-1,1,e\left(\frac{12}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 2420 }(1171, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{39}{55}\right)\) |