Basic properties
| Modulus: | \(2365\) | |
| Conductor: | \(2365\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2365.dk
\(\chi_{2365}(9,\cdot)\) \(\chi_{2365}(14,\cdot)\) \(\chi_{2365}(124,\cdot)\) \(\chi_{2365}(169,\cdot)\) \(\chi_{2365}(224,\cdot)\) \(\chi_{2365}(229,\cdot)\) \(\chi_{2365}(289,\cdot)\) \(\chi_{2365}(324,\cdot)\) \(\chi_{2365}(339,\cdot)\) \(\chi_{2365}(444,\cdot)\) \(\chi_{2365}(454,\cdot)\) \(\chi_{2365}(504,\cdot)\) \(\chi_{2365}(554,\cdot)\) \(\chi_{2365}(599,\cdot)\) \(\chi_{2365}(619,\cdot)\) \(\chi_{2365}(654,\cdot)\) \(\chi_{2365}(669,\cdot)\) \(\chi_{2365}(719,\cdot)\) \(\chi_{2365}(784,\cdot)\) \(\chi_{2365}(834,\cdot)\) \(\chi_{2365}(874,\cdot)\) \(\chi_{2365}(884,\cdot)\) \(\chi_{2365}(984,\cdot)\) \(\chi_{2365}(999,\cdot)\) \(\chi_{2365}(1004,\cdot)\) \(\chi_{2365}(1049,\cdot)\) \(\chi_{2365}(1149,\cdot)\) \(\chi_{2365}(1214,\cdot)\) \(\chi_{2365}(1219,\cdot)\) \(\chi_{2365}(1314,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 2365 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{79}{105}\right)\) |