Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(315\) | 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.em
\(\chi_{4009}(4,\cdot)\) \(\chi_{4009}(6,\cdot)\) \(\chi_{4009}(9,\cdot)\) \(\chi_{4009}(16,\cdot)\) \(\chi_{4009}(24,\cdot)\) \(\chi_{4009}(36,\cdot)\) \(\chi_{4009}(44,\cdot)\) \(\chi_{4009}(66,\cdot)\) \(\chi_{4009}(81,\cdot)\) \(\chi_{4009}(99,\cdot)\) \(\chi_{4009}(139,\cdot)\) \(\chi_{4009}(176,\cdot)\) \(\chi_{4009}(215,\cdot)\) \(\chi_{4009}(256,\cdot)\) \(\chi_{4009}(264,\cdot)\) \(\chi_{4009}(289,\cdot)\) \(\chi_{4009}(310,\cdot)\) \(\chi_{4009}(347,\cdot)\) \(\chi_{4009}(365,\cdot)\) \(\chi_{4009}(415,\cdot)\) \(\chi_{4009}(484,\cdot)\) \(\chi_{4009}(491,\cdot)\) \(\chi_{4009}(500,\cdot)\) \(\chi_{4009}(541,\cdot)\) \(\chi_{4009}(548,\cdot)\) \(\chi_{4009}(576,\cdot)\) \(\chi_{4009}(594,\cdot)\) \(\chi_{4009}(670,\cdot)\) \(\chi_{4009}(689,\cdot)\) \(\chi_{4009}(726,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{315})$ |
Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{105}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{315}\right)\) | \(e\left(\frac{269}{315}\right)\) | \(e\left(\frac{76}{315}\right)\) | \(e\left(\frac{11}{315}\right)\) | \(e\left(\frac{307}{315}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{223}{315}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{92}{105}\right)\) |