Basic properties
Modulus: | \(4730\) | |
Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2365}(1073,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dg
\(\chi_{4730}(107,\cdot)\) \(\chi_{4730}(127,\cdot)\) \(\chi_{4730}(183,\cdot)\) \(\chi_{4730}(193,\cdot)\) \(\chi_{4730}(293,\cdot)\) \(\chi_{4730}(403,\cdot)\) \(\chi_{4730}(557,\cdot)\) \(\chi_{4730}(563,\cdot)\) \(\chi_{4730}(613,\cdot)\) \(\chi_{4730}(623,\cdot)\) \(\chi_{4730}(723,\cdot)\) \(\chi_{4730}(833,\cdot)\) \(\chi_{4730}(987,\cdot)\) \(\chi_{4730}(1053,\cdot)\) \(\chi_{4730}(1073,\cdot)\) \(\chi_{4730}(1337,\cdot)\) \(\chi_{4730}(1503,\cdot)\) \(\chi_{4730}(1767,\cdot)\) \(\chi_{4730}(1817,\cdot)\) \(\chi_{4730}(1927,\cdot)\) \(\chi_{4730}(1933,\cdot)\) \(\chi_{4730}(2037,\cdot)\) \(\chi_{4730}(2197,\cdot)\) \(\chi_{4730}(2257,\cdot)\) \(\chi_{4730}(2283,\cdot)\) \(\chi_{4730}(2713,\cdot)\) \(\chi_{4730}(2763,\cdot)\) \(\chi_{4730}(2873,\cdot)\) \(\chi_{4730}(2983,\cdot)\) \(\chi_{4730}(3137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{9}{10}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(1073, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{23}{35}\right)\) |