Basic properties
Modulus: | \(6013\) | |
Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(858\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6013.cx
\(\chi_{6013}(75,\cdot)\) \(\chi_{6013}(115,\cdot)\) \(\chi_{6013}(143,\cdot)\) \(\chi_{6013}(145,\cdot)\) \(\chi_{6013}(171,\cdot)\) \(\chi_{6013}(199,\cdot)\) \(\chi_{6013}(241,\cdot)\) \(\chi_{6013}(255,\cdot)\) \(\chi_{6013}(292,\cdot)\) \(\chi_{6013}(332,\cdot)\) \(\chi_{6013}(360,\cdot)\) \(\chi_{6013}(388,\cdot)\) \(\chi_{6013}(404,\cdot)\) \(\chi_{6013}(418,\cdot)\) \(\chi_{6013}(453,\cdot)\) \(\chi_{6013}(458,\cdot)\) \(\chi_{6013}(472,\cdot)\) \(\chi_{6013}(488,\cdot)\) \(\chi_{6013}(493,\cdot)\) \(\chi_{6013}(495,\cdot)\) \(\chi_{6013}(516,\cdot)\) \(\chi_{6013}(537,\cdot)\) \(\chi_{6013}(556,\cdot)\) \(\chi_{6013}(558,\cdot)\) \(\chi_{6013}(628,\cdot)\) \(\chi_{6013}(640,\cdot)\) \(\chi_{6013}(649,\cdot)\) \(\chi_{6013}(691,\cdot)\) \(\chi_{6013}(696,\cdot)\) \(\chi_{6013}(710,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{429})$ |
Fixed field: | Number field defined by a degree 858 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{281}{286}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6013 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{557}{858}\right)\) | \(e\left(\frac{323}{429}\right)\) | \(e\left(\frac{128}{429}\right)\) | \(e\left(\frac{719}{858}\right)\) | \(e\left(\frac{115}{286}\right)\) | \(e\left(\frac{271}{286}\right)\) | \(e\left(\frac{217}{429}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{487}{858}\right)\) | \(e\left(\frac{2}{39}\right)\) |