Basic properties
| Modulus: | \(2303\) | |
| Conductor: | \(2303\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(966\) | 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 2303.bf
\(\chi_{2303}(3,\cdot)\) \(\chi_{2303}(12,\cdot)\) \(\chi_{2303}(17,\cdot)\) \(\chi_{2303}(24,\cdot)\) \(\chi_{2303}(54,\cdot)\) \(\chi_{2303}(59,\cdot)\) \(\chi_{2303}(61,\cdot)\) \(\chi_{2303}(75,\cdot)\) \(\chi_{2303}(89,\cdot)\) \(\chi_{2303}(96,\cdot)\) \(\chi_{2303}(101,\cdot)\) \(\chi_{2303}(103,\cdot)\) \(\chi_{2303}(108,\cdot)\) \(\chi_{2303}(110,\cdot)\) \(\chi_{2303}(115,\cdot)\) \(\chi_{2303}(122,\cdot)\) \(\chi_{2303}(131,\cdot)\) \(\chi_{2303}(136,\cdot)\) \(\chi_{2303}(143,\cdot)\) \(\chi_{2303}(145,\cdot)\) \(\chi_{2303}(150,\cdot)\) \(\chi_{2303}(157,\cdot)\) \(\chi_{2303}(159,\cdot)\) \(\chi_{2303}(173,\cdot)\) \(\chi_{2303}(192,\cdot)\) \(\chi_{2303}(194,\cdot)\) \(\chi_{2303}(206,\cdot)\) \(\chi_{2303}(213,\cdot)\) \(\chi_{2303}(220,\cdot)\) \(\chi_{2303}(222,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((2257,99)\) → \((e\left(\frac{11}{42}\right),e\left(\frac{2}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2303 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{181}{483}\right)\) | \(e\left(\frac{1}{966}\right)\) | \(e\left(\frac{362}{483}\right)\) | \(e\left(\frac{659}{966}\right)\) | \(e\left(\frac{121}{322}\right)\) | \(e\left(\frac{20}{161}\right)\) | \(e\left(\frac{1}{483}\right)\) | \(e\left(\frac{55}{966}\right)\) | \(e\left(\frac{41}{483}\right)\) | \(e\left(\frac{725}{966}\right)\) |