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 \(\chi_{1501}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cv
\(\chi_{6004}(49,\cdot)\) \(\chi_{6004}(657,\cdot)\) \(\chi_{6004}(885,\cdot)\) \(\chi_{6004}(957,\cdot)\) \(\chi_{6004}(961,\cdot)\) \(\chi_{6004}(1337,\cdot)\) \(\chi_{6004}(2173,\cdot)\) \(\chi_{6004}(2177,\cdot)\) \(\chi_{6004}(2401,\cdot)\) \(\chi_{6004}(2705,\cdot)\) \(\chi_{6004}(2785,\cdot)\) \(\chi_{6004}(3085,\cdot)\) \(\chi_{6004}(3241,\cdot)\) \(\chi_{6004}(3921,\cdot)\) \(\chi_{6004}(4001,\cdot)\) \(\chi_{6004}(4153,\cdot)\) \(\chi_{6004}(4229,\cdot)\) \(\chi_{6004}(4377,\cdot)\) \(\chi_{6004}(4381,\cdot)\) \(\chi_{6004}(4529,\cdot)\) \(\chi_{6004}(4909,\cdot)\) \(\chi_{6004}(5061,\cdot)\) \(\chi_{6004}(5365,\cdot)\) \(\chi_{6004}(5369,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{14}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) |