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 \(\chi_{2365}(753,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.df
\(\chi_{4730}(27,\cdot)\) \(\chi_{4730}(113,\cdot)\) \(\chi_{4730}(137,\cdot)\) \(\chi_{4730}(223,\cdot)\) \(\chi_{4730}(247,\cdot)\) \(\chi_{4730}(323,\cdot)\) \(\chi_{4730}(333,\cdot)\) \(\chi_{4730}(383,\cdot)\) \(\chi_{4730}(543,\cdot)\) \(\chi_{4730}(647,\cdot)\) \(\chi_{4730}(653,\cdot)\) \(\chi_{4730}(753,\cdot)\) \(\chi_{4730}(763,\cdot)\) \(\chi_{4730}(973,\cdot)\) \(\chi_{4730}(1083,\cdot)\) \(\chi_{4730}(1193,\cdot)\) \(\chi_{4730}(1527,\cdot)\) \(\chi_{4730}(1587,\cdot)\) \(\chi_{4730}(1593,\cdot)\) \(\chi_{4730}(1747,\cdot)\) \(\chi_{4730}(1857,\cdot)\) \(\chi_{4730}(1967,\cdot)\) \(\chi_{4730}(2017,\cdot)\) \(\chi_{4730}(2447,\cdot)\) \(\chi_{4730}(2473,\cdot)\) \(\chi_{4730}(2533,\cdot)\) \(\chi_{4730}(2693,\cdot)\) \(\chi_{4730}(2797,\cdot)\) \(\chi_{4730}(2803,\cdot)\) \(\chi_{4730}(2913,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{2}{5}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(753, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{33}{35}\right)\) |