Basic properties
| Modulus: | \(4504\) | |
| Conductor: | \(4504\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(562\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4504.l
\(\chi_{4504}(3,\cdot)\) \(\chi_{4504}(11,\cdot)\) \(\chi_{4504}(19,\cdot)\) \(\chi_{4504}(27,\cdot)\) \(\chi_{4504}(51,\cdot)\) \(\chi_{4504}(59,\cdot)\) \(\chi_{4504}(67,\cdot)\) \(\chi_{4504}(75,\cdot)\) \(\chi_{4504}(91,\cdot)\) \(\chi_{4504}(99,\cdot)\) \(\chi_{4504}(107,\cdot)\) \(\chi_{4504}(147,\cdot)\) \(\chi_{4504}(155,\cdot)\) \(\chi_{4504}(171,\cdot)\) \(\chi_{4504}(179,\cdot)\) \(\chi_{4504}(187,\cdot)\) \(\chi_{4504}(211,\cdot)\) \(\chi_{4504}(243,\cdot)\) \(\chi_{4504}(251,\cdot)\) \(\chi_{4504}(275,\cdot)\) \(\chi_{4504}(299,\cdot)\) \(\chi_{4504}(323,\cdot)\) \(\chi_{4504}(339,\cdot)\) \(\chi_{4504}(347,\cdot)\) \(\chi_{4504}(363,\cdot)\) \(\chi_{4504}(379,\cdot)\) \(\chi_{4504}(395,\cdot)\) \(\chi_{4504}(411,\cdot)\) \(\chi_{4504}(427,\cdot)\) \(\chi_{4504}(435,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{281})$ |
| Fixed field: | Number field defined by a degree 562 polynomial (not computed) |
Values on generators
\((1127,2253,2817)\) → \((-1,-1,e\left(\frac{233}{281}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4504 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{131}{281}\right)\) | \(e\left(\frac{481}{562}\right)\) | \(e\left(\frac{165}{562}\right)\) | \(e\left(\frac{262}{281}\right)\) | \(e\left(\frac{103}{281}\right)\) | \(e\left(\frac{229}{562}\right)\) | \(e\left(\frac{181}{562}\right)\) | \(e\left(\frac{280}{281}\right)\) | \(e\left(\frac{40}{281}\right)\) | \(e\left(\frac{427}{562}\right)\) |