Basic properties
| Modulus: | \(4730\) | |
| Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2365}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dd
\(\chi_{4730}(47,\cdot)\) \(\chi_{4730}(97,\cdot)\) \(\chi_{4730}(207,\cdot)\) \(\chi_{4730}(213,\cdot)\) \(\chi_{4730}(317,\cdot)\) \(\chi_{4730}(477,\cdot)\) \(\chi_{4730}(537,\cdot)\) \(\chi_{4730}(643,\cdot)\) \(\chi_{4730}(907,\cdot)\) \(\chi_{4730}(993,\cdot)\) \(\chi_{4730}(1043,\cdot)\) \(\chi_{4730}(1153,\cdot)\) \(\chi_{4730}(1263,\cdot)\) \(\chi_{4730}(1417,\cdot)\) \(\chi_{4730}(1423,\cdot)\) \(\chi_{4730}(1483,\cdot)\) \(\chi_{4730}(1853,\cdot)\) \(\chi_{4730}(2247,\cdot)\) \(\chi_{4730}(2357,\cdot)\) \(\chi_{4730}(2363,\cdot)\) \(\chi_{4730}(2467,\cdot)\) \(\chi_{4730}(2627,\cdot)\) \(\chi_{4730}(2677,\cdot)\) \(\chi_{4730}(2687,\cdot)\) \(\chi_{4730}(2787,\cdot)\) \(\chi_{4730}(2897,\cdot)\) \(\chi_{4730}(3107,\cdot)\) \(\chi_{4730}(3117,\cdot)\) \(\chi_{4730}(3193,\cdot)\) \(\chi_{4730}(3217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((i,e\left(\frac{4}{5}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{97}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) |