Basic properties
| Modulus: | \(3784\) | |
| Conductor: | \(3784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 3784.em
\(\chi_{3784}(203,\cdot)\) \(\chi_{3784}(267,\cdot)\) \(\chi_{3784}(339,\cdot)\) \(\chi_{3784}(411,\cdot)\) \(\chi_{3784}(427,\cdot)\) \(\chi_{3784}(443,\cdot)\) \(\chi_{3784}(531,\cdot)\) \(\chi_{3784}(619,\cdot)\) \(\chi_{3784}(883,\cdot)\) \(\chi_{3784}(955,\cdot)\) \(\chi_{3784}(971,\cdot)\) \(\chi_{3784}(1027,\cdot)\) \(\chi_{3784}(1115,\cdot)\) \(\chi_{3784}(1131,\cdot)\) \(\chi_{3784}(1171,\cdot)\) \(\chi_{3784}(1219,\cdot)\) \(\chi_{3784}(1235,\cdot)\) \(\chi_{3784}(1307,\cdot)\) \(\chi_{3784}(1347,\cdot)\) \(\chi_{3784}(1571,\cdot)\) \(\chi_{3784}(1643,\cdot)\) \(\chi_{3784}(1659,\cdot)\) \(\chi_{3784}(1787,\cdot)\) \(\chi_{3784}(1819,\cdot)\) \(\chi_{3784}(1907,\cdot)\) \(\chi_{3784}(1923,\cdot)\) \(\chi_{3784}(1995,\cdot)\) \(\chi_{3784}(2203,\cdot)\) \(\chi_{3784}(2259,\cdot)\) \(\chi_{3784}(2347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2839,1893,1377,89)\) → \((-1,-1,e\left(\frac{3}{5}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3784 }(1307, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) |