Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(630\) | 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.ep
\(\chi_{4009}(41,\cdot)\) \(\chi_{4009}(91,\cdot)\) \(\chi_{4009}(127,\cdot)\) \(\chi_{4009}(165,\cdot)\) \(\chi_{4009}(166,\cdot)\) \(\chi_{4009}(268,\cdot)\) \(\chi_{4009}(338,\cdot)\) \(\chi_{4009}(344,\cdot)\) \(\chi_{4009}(356,\cdot)\) \(\chi_{4009}(376,\cdot)\) \(\chi_{4009}(402,\cdot)\) \(\chi_{4009}(413,\cdot)\) \(\chi_{4009}(451,\cdot)\) \(\chi_{4009}(470,\cdot)\) \(\chi_{4009}(507,\cdot)\) \(\chi_{4009}(534,\cdot)\) \(\chi_{4009}(564,\cdot)\) \(\chi_{4009}(580,\cdot)\) \(\chi_{4009}(584,\cdot)\) \(\chi_{4009}(603,\cdot)\) \(\chi_{4009}(629,\cdot)\) \(\chi_{4009}(640,\cdot)\) \(\chi_{4009}(705,\cdot)\) \(\chi_{4009}(718,\cdot)\) \(\chi_{4009}(725,\cdot)\) \(\chi_{4009}(774,\cdot)\) \(\chi_{4009}(775,\cdot)\) \(\chi_{4009}(782,\cdot)\) \(\chi_{4009}(793,\cdot)\) \(\chi_{4009}(800,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{17}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{315}\right)\) | \(e\left(\frac{274}{315}\right)\) | \(e\left(\frac{191}{315}\right)\) | \(e\left(\frac{76}{315}\right)\) | \(e\left(\frac{212}{315}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{233}{315}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{82}{105}\right)\) |