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 \(\chi_{2365}(828,\cdot)\) | 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
\((947,431,1981)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(3193, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) |