Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ds
\(\chi_{6004}(37,\cdot)\) \(\chi_{6004}(113,\cdot)\) \(\chi_{6004}(265,\cdot)\) \(\chi_{6004}(797,\cdot)\) \(\chi_{6004}(1025,\cdot)\) \(\chi_{6004}(1101,\cdot)\) \(\chi_{6004}(1253,\cdot)\) \(\chi_{6004}(1481,\cdot)\) \(\chi_{6004}(1633,\cdot)\) \(\chi_{6004}(1785,\cdot)\) \(\chi_{6004}(2089,\cdot)\) \(\chi_{6004}(2241,\cdot)\) \(\chi_{6004}(3077,\cdot)\) \(\chi_{6004}(3305,\cdot)\) \(\chi_{6004}(3381,\cdot)\) \(\chi_{6004}(3457,\cdot)\) \(\chi_{6004}(3609,\cdot)\) \(\chi_{6004}(3761,\cdot)\) \(\chi_{6004}(3989,\cdot)\) \(\chi_{6004}(4217,\cdot)\) \(\chi_{6004}(4825,\cdot)\) \(\chi_{6004}(4901,\cdot)\) \(\chi_{6004}(5205,\cdot)\) \(\chi_{6004}(5889,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,-1,e\left(\frac{19}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) |