Basic properties
Modulus: | \(3021\) | |
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 \(\chi_{1007}(938,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3021.bx
\(\chi_{3021}(7,\cdot)\) \(\chi_{3021}(64,\cdot)\) \(\chi_{3021}(163,\cdot)\) \(\chi_{3021}(520,\cdot)\) \(\chi_{3021}(676,\cdot)\) \(\chi_{3021}(748,\cdot)\) \(\chi_{3021}(961,\cdot)\) \(\chi_{3021}(1018,\cdot)\) \(\chi_{3021}(1204,\cdot)\) \(\chi_{3021}(1474,\cdot)\) \(\chi_{3021}(1546,\cdot)\) \(\chi_{3021}(1660,\cdot)\) \(\chi_{3021}(1702,\cdot)\) \(\chi_{3021}(1774,\cdot)\) \(\chi_{3021}(1831,\cdot)\) \(\chi_{3021}(1945,\cdot)\) \(\chi_{3021}(2158,\cdot)\) \(\chi_{3021}(2230,\cdot)\) \(\chi_{3021}(2500,\cdot)\) \(\chi_{3021}(2614,\cdot)\) \(\chi_{3021}(2728,\cdot)\) \(\chi_{3021}(2743,\cdot)\) \(\chi_{3021}(2785,\cdot)\) \(\chi_{3021}(2899,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,1750,2281)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{15}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 3021 }(1945, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) |