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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.dm
\(\chi_{2695}(4,\cdot)\) \(\chi_{2695}(9,\cdot)\) \(\chi_{2695}(114,\cdot)\) \(\chi_{2695}(179,\cdot)\) \(\chi_{2695}(284,\cdot)\) \(\chi_{2695}(289,\cdot)\) \(\chi_{2695}(389,\cdot)\) \(\chi_{2695}(394,\cdot)\) \(\chi_{2695}(499,\cdot)\) \(\chi_{2695}(564,\cdot)\) \(\chi_{2695}(599,\cdot)\) \(\chi_{2695}(669,\cdot)\) \(\chi_{2695}(674,\cdot)\) \(\chi_{2695}(709,\cdot)\) \(\chi_{2695}(774,\cdot)\) \(\chi_{2695}(779,\cdot)\) \(\chi_{2695}(884,\cdot)\) \(\chi_{2695}(984,\cdot)\) \(\chi_{2695}(1054,\cdot)\) \(\chi_{2695}(1094,\cdot)\) \(\chi_{2695}(1159,\cdot)\) \(\chi_{2695}(1164,\cdot)\) \(\chi_{2695}(1269,\cdot)\) \(\chi_{2695}(1334,\cdot)\) \(\chi_{2695}(1369,\cdot)\) \(\chi_{2695}(1444,\cdot)\) \(\chi_{2695}(1479,\cdot)\) \(\chi_{2695}(1544,\cdot)\) \(\chi_{2695}(1654,\cdot)\) \(\chi_{2695}(1719,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2157,1816,981)\) → \((-1,e\left(\frac{5}{21}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{53}{210}\right)\) |