Basic properties
Modulus: | \(1007\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 1007.z
\(\chi_{1007}(7,\cdot)\) \(\chi_{1007}(11,\cdot)\) \(\chi_{1007}(64,\cdot)\) \(\chi_{1007}(144,\cdot)\) \(\chi_{1007}(163,\cdot)\) \(\chi_{1007}(197,\cdot)\) \(\chi_{1007}(216,\cdot)\) \(\chi_{1007}(467,\cdot)\) \(\chi_{1007}(486,\cdot)\) \(\chi_{1007}(520,\cdot)\) \(\chi_{1007}(539,\cdot)\) \(\chi_{1007}(600,\cdot)\) \(\chi_{1007}(653,\cdot)\) \(\chi_{1007}(676,\cdot)\) \(\chi_{1007}(695,\cdot)\) \(\chi_{1007}(714,\cdot)\) \(\chi_{1007}(729,\cdot)\) \(\chi_{1007}(748,\cdot)\) \(\chi_{1007}(767,\cdot)\) \(\chi_{1007}(771,\cdot)\) \(\chi_{1007}(824,\cdot)\) \(\chi_{1007}(885,\cdot)\) \(\chi_{1007}(938,\cdot)\) \(\chi_{1007}(961,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,267)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1007 }(144, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) |