Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | 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 4009.ec
\(\chi_{4009}(8,\cdot)\) \(\chi_{4009}(27,\cdot)\) \(\chi_{4009}(198,\cdot)\) \(\chi_{4009}(297,\cdot)\) \(\chi_{4009}(335,\cdot)\) \(\chi_{4009}(411,\cdot)\) \(\chi_{4009}(430,\cdot)\) \(\chi_{4009}(449,\cdot)\) \(\chi_{4009}(464,\cdot)\) \(\chi_{4009}(620,\cdot)\) \(\chi_{4009}(730,\cdot)\) \(\chi_{4009}(768,\cdot)\) \(\chi_{4009}(886,\cdot)\) \(\chi_{4009}(1152,\cdot)\) \(\chi_{4009}(1190,\cdot)\) \(\chi_{4009}(1395,\cdot)\) \(\chi_{4009}(1452,\cdot)\) \(\chi_{4009}(1566,\cdot)\) \(\chi_{4009}(1623,\cdot)\) \(\chi_{4009}(1756,\cdot)\) \(\chi_{4009}(1817,\cdot)\) \(\chi_{4009}(1874,\cdot)\) \(\chi_{4009}(1927,\cdot)\) \(\chi_{4009}(1988,\cdot)\) \(\chi_{4009}(2045,\cdot)\) \(\chi_{4009}(2178,\cdot)\) \(\chi_{4009}(2212,\cdot)\) \(\chi_{4009}(2349,\cdot)\) \(\chi_{4009}(2592,\cdot)\) \(\chi_{4009}(2630,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{43}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{18}{35}\right)\) |