Basic properties
Modulus: | \(6013\) | |
Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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.bj
\(\chi_{6013}(100,\cdot)\) \(\chi_{6013}(478,\cdot)\) \(\chi_{6013}(555,\cdot)\) \(\chi_{6013}(718,\cdot)\) \(\chi_{6013}(849,\cdot)\) \(\chi_{6013}(1362,\cdot)\) \(\chi_{6013}(1383,\cdot)\) \(\chi_{6013}(1577,\cdot)\) \(\chi_{6013}(2181,\cdot)\) \(\chi_{6013}(2221,\cdot)\) \(\chi_{6013}(2242,\cdot)\) \(\chi_{6013}(2951,\cdot)\) \(\chi_{6013}(3040,\cdot)\) \(\chi_{6013}(3350,\cdot)\) \(\chi_{6013}(3560,\cdot)\) \(\chi_{6013}(3810,\cdot)\) \(\chi_{6013}(3987,\cdot)\) \(\chi_{6013}(4209,\cdot)\) \(\chi_{6013}(4419,\cdot)\) \(\chi_{6013}(4846,\cdot)\) \(\chi_{6013}(5254,\cdot)\) \(\chi_{6013}(5632,\cdot)\) \(\chi_{6013}(5709,\cdot)\) \(\chi_{6013}(6003,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((5155,3438)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6013 }(2242, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) |