Basic properties
Modulus: | \(6004\) | |
Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1501}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cu
\(\chi_{6004}(45,\cdot)\) \(\chi_{6004}(121,\cdot)\) \(\chi_{6004}(273,\cdot)\) \(\chi_{6004}(277,\cdot)\) \(\chi_{6004}(505,\cdot)\) \(\chi_{6004}(809,\cdot)\) \(\chi_{6004}(1189,\cdot)\) \(\chi_{6004}(1261,\cdot)\) \(\chi_{6004}(1945,\cdot)\) \(\chi_{6004}(2025,\cdot)\) \(\chi_{6004}(2481,\cdot)\) \(\chi_{6004}(2553,\cdot)\) \(\chi_{6004}(2633,\cdot)\) \(\chi_{6004}(2781,\cdot)\) \(\chi_{6004}(2857,\cdot)\) \(\chi_{6004}(3013,\cdot)\) \(\chi_{6004}(3165,\cdot)\) \(\chi_{6004}(3469,\cdot)\) \(\chi_{6004}(4073,\cdot)\) \(\chi_{6004}(4681,\cdot)\) \(\chi_{6004}(5065,\cdot)\) \(\chi_{6004}(5137,\cdot)\) \(\chi_{6004}(5445,\cdot)\) \(\chi_{6004}(5897,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{32}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(1\) |