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.et
\(\chi_{4009}(2,\cdot)\) \(\chi_{4009}(3,\cdot)\) \(\chi_{4009}(22,\cdot)\) \(\chi_{4009}(29,\cdot)\) \(\chi_{4009}(48,\cdot)\) \(\chi_{4009}(72,\cdot)\) \(\chi_{4009}(108,\cdot)\) \(\chi_{4009}(116,\cdot)\) \(\chi_{4009}(155,\cdot)\) \(\chi_{4009}(162,\cdot)\) \(\chi_{4009}(167,\cdot)\) \(\chi_{4009}(174,\cdot)\) \(\chi_{4009}(181,\cdot)\) \(\chi_{4009}(205,\cdot)\) \(\chi_{4009}(250,\cdot)\) \(\chi_{4009}(317,\cdot)\) \(\chi_{4009}(319,\cdot)\) \(\chi_{4009}(352,\cdot)\) \(\chi_{4009}(363,\cdot)\) \(\chi_{4009}(371,\cdot)\) \(\chi_{4009}(375,\cdot)\) \(\chi_{4009}(439,\cdot)\) \(\chi_{4009}(497,\cdot)\) \(\chi_{4009}(528,\cdot)\) \(\chi_{4009}(553,\cdot)\) \(\chi_{4009}(668,\cdot)\) \(\chi_{4009}(724,\cdot)\) \(\chi_{4009}(751,\cdot)\) \(\chi_{4009}(763,\cdot)\) \(\chi_{4009}(792,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{1}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{315}\right)\) | \(e\left(\frac{292}{315}\right)\) | \(e\left(\frac{38}{315}\right)\) | \(e\left(\frac{163}{315}\right)\) | \(e\left(\frac{311}{315}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{269}{315}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{46}{105}\right)\) |