Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(2695\) | 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 2695.dl
\(\chi_{2695}(59,\cdot)\) \(\chi_{2695}(124,\cdot)\) \(\chi_{2695}(159,\cdot)\) \(\chi_{2695}(229,\cdot)\) \(\chi_{2695}(234,\cdot)\) \(\chi_{2695}(269,\cdot)\) \(\chi_{2695}(334,\cdot)\) \(\chi_{2695}(339,\cdot)\) \(\chi_{2695}(444,\cdot)\) \(\chi_{2695}(544,\cdot)\) \(\chi_{2695}(614,\cdot)\) \(\chi_{2695}(654,\cdot)\) \(\chi_{2695}(719,\cdot)\) \(\chi_{2695}(724,\cdot)\) \(\chi_{2695}(829,\cdot)\) \(\chi_{2695}(894,\cdot)\) \(\chi_{2695}(929,\cdot)\) \(\chi_{2695}(1004,\cdot)\) \(\chi_{2695}(1039,\cdot)\) \(\chi_{2695}(1104,\cdot)\) \(\chi_{2695}(1214,\cdot)\) \(\chi_{2695}(1279,\cdot)\) \(\chi_{2695}(1314,\cdot)\) \(\chi_{2695}(1384,\cdot)\) \(\chi_{2695}(1389,\cdot)\) \(\chi_{2695}(1424,\cdot)\) \(\chi_{2695}(1494,\cdot)\) \(\chi_{2695}(1664,\cdot)\) \(\chi_{2695}(1699,\cdot)\) \(\chi_{2695}(1769,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2157,1816,981)\) → \((-1,e\left(\frac{31}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(829, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) |