Basic properties
| Modulus: | \(1021\) | |
| Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1021.p
\(\chi_{1021}(13,\cdot)\) \(\chi_{1021}(32,\cdot)\) \(\chi_{1021}(39,\cdot)\) \(\chi_{1021}(96,\cdot)\) \(\chi_{1021}(101,\cdot)\) \(\chi_{1021}(112,\cdot)\) \(\chi_{1021}(117,\cdot)\) \(\chi_{1021}(155,\cdot)\) \(\chi_{1021}(157,\cdot)\) \(\chi_{1021}(288,\cdot)\) \(\chi_{1021}(303,\cdot)\) \(\chi_{1021}(336,\cdot)\) \(\chi_{1021}(351,\cdot)\) \(\chi_{1021}(392,\cdot)\) \(\chi_{1021}(465,\cdot)\) \(\chi_{1021}(471,\cdot)\) \(\chi_{1021}(550,\cdot)\) \(\chi_{1021}(556,\cdot)\) \(\chi_{1021}(629,\cdot)\) \(\chi_{1021}(670,\cdot)\) \(\chi_{1021}(685,\cdot)\) \(\chi_{1021}(718,\cdot)\) \(\chi_{1021}(733,\cdot)\) \(\chi_{1021}(864,\cdot)\) \(\chi_{1021}(866,\cdot)\) \(\chi_{1021}(904,\cdot)\) \(\chi_{1021}(909,\cdot)\) \(\chi_{1021}(920,\cdot)\) \(\chi_{1021}(925,\cdot)\) \(\chi_{1021}(982,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\(10\) → \(e\left(\frac{11}{68}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1021 }(288, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{10}{17}\right)\) |