Basic properties
| Modulus: | \(4704\) | |
| Conductor: | \(4704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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 4704.ef
\(\chi_{4704}(125,\cdot)\) \(\chi_{4704}(461,\cdot)\) \(\chi_{4704}(629,\cdot)\) \(\chi_{4704}(797,\cdot)\) \(\chi_{4704}(965,\cdot)\) \(\chi_{4704}(1133,\cdot)\) \(\chi_{4704}(1301,\cdot)\) \(\chi_{4704}(1637,\cdot)\) \(\chi_{4704}(1805,\cdot)\) \(\chi_{4704}(1973,\cdot)\) \(\chi_{4704}(2141,\cdot)\) \(\chi_{4704}(2309,\cdot)\) \(\chi_{4704}(2477,\cdot)\) \(\chi_{4704}(2813,\cdot)\) \(\chi_{4704}(2981,\cdot)\) \(\chi_{4704}(3149,\cdot)\) \(\chi_{4704}(3317,\cdot)\) \(\chi_{4704}(3485,\cdot)\) \(\chi_{4704}(3653,\cdot)\) \(\chi_{4704}(3989,\cdot)\) \(\chi_{4704}(4157,\cdot)\) \(\chi_{4704}(4325,\cdot)\) \(\chi_{4704}(4493,\cdot)\) \(\chi_{4704}(4661,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,1765,3137,4609)\) → \((1,e\left(\frac{3}{8}\right),-1,e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 4704 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(-1\) | \(e\left(\frac{37}{56}\right)\) |