Basic properties
Modulus: | \(6004\) | |
Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1501}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.df
\(\chi_{6004}(65,\cdot)\) \(\chi_{6004}(141,\cdot)\) \(\chi_{6004}(749,\cdot)\) \(\chi_{6004}(1285,\cdot)\) \(\chi_{6004}(1361,\cdot)\) \(\chi_{6004}(1509,\cdot)\) \(\chi_{6004}(2121,\cdot)\) \(\chi_{6004}(2197,\cdot)\) \(\chi_{6004}(2501,\cdot)\) \(\chi_{6004}(2653,\cdot)\) \(\chi_{6004}(3181,\cdot)\) \(\chi_{6004}(3257,\cdot)\) \(\chi_{6004}(3261,\cdot)\) \(\chi_{6004}(3565,\cdot)\) \(\chi_{6004}(4017,\cdot)\) \(\chi_{6004}(4093,\cdot)\) \(\chi_{6004}(4173,\cdot)\) \(\chi_{6004}(4249,\cdot)\) \(\chi_{6004}(4397,\cdot)\) \(\chi_{6004}(4549,\cdot)\) \(\chi_{6004}(4857,\cdot)\) \(\chi_{6004}(5157,\cdot)\) \(\chi_{6004}(5461,\cdot)\) \(\chi_{6004}(5617,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{3}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(65, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) |