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 \(\chi_{1007}(486,\cdot)\) | 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
\((2015,1750,2281)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{17}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3021 }(2500, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) |