Basic properties
Modulus: | \(6004\) | |
Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 6004.dv
\(\chi_{6004}(179,\cdot)\) \(\chi_{6004}(255,\cdot)\) \(\chi_{6004}(259,\cdot)\) \(\chi_{6004}(563,\cdot)\) \(\chi_{6004}(1015,\cdot)\) \(\chi_{6004}(1091,\cdot)\) \(\chi_{6004}(1171,\cdot)\) \(\chi_{6004}(1247,\cdot)\) \(\chi_{6004}(1395,\cdot)\) \(\chi_{6004}(1547,\cdot)\) \(\chi_{6004}(1855,\cdot)\) \(\chi_{6004}(2155,\cdot)\) \(\chi_{6004}(2459,\cdot)\) \(\chi_{6004}(2615,\cdot)\) \(\chi_{6004}(3067,\cdot)\) \(\chi_{6004}(3143,\cdot)\) \(\chi_{6004}(3751,\cdot)\) \(\chi_{6004}(4287,\cdot)\) \(\chi_{6004}(4363,\cdot)\) \(\chi_{6004}(4511,\cdot)\) \(\chi_{6004}(5123,\cdot)\) \(\chi_{6004}(5199,\cdot)\) \(\chi_{6004}(5503,\cdot)\) \(\chi_{6004}(5655,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) |