Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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.dn
\(\chi_{4009}(30,\cdot)\) \(\chi_{4009}(49,\cdot)\) \(\chi_{4009}(163,\cdot)\) \(\chi_{4009}(182,\cdot)\) \(\chi_{4009}(220,\cdot)\) \(\chi_{4009}(235,\cdot)\) \(\chi_{4009}(277,\cdot)\) \(\chi_{4009}(292,\cdot)\) \(\chi_{4009}(387,\cdot)\) \(\chi_{4009}(467,\cdot)\) \(\chi_{4009}(558,\cdot)\) \(\chi_{4009}(695,\cdot)\) \(\chi_{4009}(752,\cdot)\) \(\chi_{4009}(805,\cdot)\) \(\chi_{4009}(881,\cdot)\) \(\chi_{4009}(900,\cdot)\) \(\chi_{4009}(1033,\cdot)\) \(\chi_{4009}(1052,\cdot)\) \(\chi_{4009}(1071,\cdot)\) \(\chi_{4009}(1075,\cdot)\) \(\chi_{4009}(1436,\cdot)\) \(\chi_{4009}(1470,\cdot)\) \(\chi_{4009}(1546,\cdot)\) \(\chi_{4009}(1603,\cdot)\) \(\chi_{4009}(1740,\cdot)\) \(\chi_{4009}(1945,\cdot)\) \(\chi_{4009}(1983,\cdot)\) \(\chi_{4009}(2215,\cdot)\) \(\chi_{4009}(2230,\cdot)\) \(\chi_{4009}(2401,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{88}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{27}{35}\right)\) |