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.eb
\(\chi_{4704}(155,\cdot)\) \(\chi_{4704}(323,\cdot)\) \(\chi_{4704}(659,\cdot)\) \(\chi_{4704}(827,\cdot)\) \(\chi_{4704}(995,\cdot)\) \(\chi_{4704}(1163,\cdot)\) \(\chi_{4704}(1331,\cdot)\) \(\chi_{4704}(1499,\cdot)\) \(\chi_{4704}(1835,\cdot)\) \(\chi_{4704}(2003,\cdot)\) \(\chi_{4704}(2171,\cdot)\) \(\chi_{4704}(2339,\cdot)\) \(\chi_{4704}(2507,\cdot)\) \(\chi_{4704}(2675,\cdot)\) \(\chi_{4704}(3011,\cdot)\) \(\chi_{4704}(3179,\cdot)\) \(\chi_{4704}(3347,\cdot)\) \(\chi_{4704}(3515,\cdot)\) \(\chi_{4704}(3683,\cdot)\) \(\chi_{4704}(3851,\cdot)\) \(\chi_{4704}(4187,\cdot)\) \(\chi_{4704}(4355,\cdot)\) \(\chi_{4704}(4523,\cdot)\) \(\chi_{4704}(4691,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,1765,3137,4609)\) → \((-1,e\left(\frac{1}{8}\right),-1,e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 4704 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(-1\) | \(e\left(\frac{31}{56}\right)\) |