Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{211}(20,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4009.dp
\(\chi_{4009}(20,\cdot)\) \(\chi_{4009}(172,\cdot)\) \(\chi_{4009}(248,\cdot)\) \(\chi_{4009}(267,\cdot)\) \(\chi_{4009}(381,\cdot)\) \(\chi_{4009}(400,\cdot)\) \(\chi_{4009}(419,\cdot)\) \(\chi_{4009}(438,\cdot)\) \(\chi_{4009}(685,\cdot)\) \(\chi_{4009}(837,\cdot)\) \(\chi_{4009}(913,\cdot)\) \(\chi_{4009}(970,\cdot)\) \(\chi_{4009}(1160,\cdot)\) \(\chi_{4009}(1312,\cdot)\) \(\chi_{4009}(1350,\cdot)\) \(\chi_{4009}(1369,\cdot)\) \(\chi_{4009}(1483,\cdot)\) \(\chi_{4009}(1521,\cdot)\) \(\chi_{4009}(1597,\cdot)\) \(\chi_{4009}(1616,\cdot)\) \(\chi_{4009}(1692,\cdot)\) \(\chi_{4009}(1768,\cdot)\) \(\chi_{4009}(1787,\cdot)\) \(\chi_{4009}(1882,\cdot)\) \(\chi_{4009}(1958,\cdot)\) \(\chi_{4009}(1977,\cdot)\) \(\chi_{4009}(2053,\cdot)\) \(\chi_{4009}(2205,\cdot)\) \(\chi_{4009}(2319,\cdot)\) \(\chi_{4009}(2357,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((1,e\left(\frac{67}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{35}\right)\) |