Basic properties
Modulus: | \(4840\) | |
Conductor: | \(2420\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2420}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4840.dp
\(\chi_{4840}(47,\cdot)\) \(\chi_{4840}(103,\cdot)\) \(\chi_{4840}(207,\cdot)\) \(\chi_{4840}(223,\cdot)\) \(\chi_{4840}(247,\cdot)\) \(\chi_{4840}(367,\cdot)\) \(\chi_{4840}(383,\cdot)\) \(\chi_{4840}(423,\cdot)\) \(\chi_{4840}(543,\cdot)\) \(\chi_{4840}(647,\cdot)\) \(\chi_{4840}(663,\cdot)\) \(\chi_{4840}(687,\cdot)\) \(\chi_{4840}(823,\cdot)\) \(\chi_{4840}(863,\cdot)\) \(\chi_{4840}(927,\cdot)\) \(\chi_{4840}(983,\cdot)\) \(\chi_{4840}(1087,\cdot)\) \(\chi_{4840}(1103,\cdot)\) \(\chi_{4840}(1127,\cdot)\) \(\chi_{4840}(1247,\cdot)\) \(\chi_{4840}(1263,\cdot)\) \(\chi_{4840}(1303,\cdot)\) \(\chi_{4840}(1367,\cdot)\) \(\chi_{4840}(1423,\cdot)\) \(\chi_{4840}(1527,\cdot)\) \(\chi_{4840}(1543,\cdot)\) \(\chi_{4840}(1567,\cdot)\) \(\chi_{4840}(1687,\cdot)\) \(\chi_{4840}(1743,\cdot)\) \(\chi_{4840}(1807,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,1,i,e\left(\frac{49}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4840 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{71}{110}\right)\) |