Basic properties
Modulus: | \(4028\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(197,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.bx
\(\chi_{4028}(197,\cdot)\) \(\chi_{4028}(653,\cdot)\) \(\chi_{4028}(729,\cdot)\) \(\chi_{4028}(885,\cdot)\) \(\chi_{4028}(961,\cdot)\) \(\chi_{4028}(1493,\cdot)\) \(\chi_{4028}(1721,\cdot)\) \(\chi_{4028}(1945,\cdot)\) \(\chi_{4028}(2021,\cdot)\) \(\chi_{4028}(2025,\cdot)\) \(\chi_{4028}(2177,\cdot)\) \(\chi_{4028}(2481,\cdot)\) \(\chi_{4028}(2553,\cdot)\) \(\chi_{4028}(2709,\cdot)\) \(\chi_{4028}(2781,\cdot)\) \(\chi_{4028}(2785,\cdot)\) \(\chi_{4028}(3085,\cdot)\) \(\chi_{4028}(3165,\cdot)\) \(\chi_{4028}(3237,\cdot)\) \(\chi_{4028}(3541,\cdot)\) \(\chi_{4028}(3621,\cdot)\) \(\chi_{4028}(3697,\cdot)\) \(\chi_{4028}(3769,\cdot)\) \(\chi_{4028}(3845,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 4028 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) |