Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.dd
\(\chi_{4009}(18,\cdot)\) \(\chi_{4009}(132,\cdot)\) \(\chi_{4009}(417,\cdot)\) \(\chi_{4009}(512,\cdot)\) \(\chi_{4009}(569,\cdot)\) \(\chi_{4009}(930,\cdot)\) \(\chi_{4009}(968,\cdot)\) \(\chi_{4009}(1044,\cdot)\) \(\chi_{4009}(1063,\cdot)\) \(\chi_{4009}(1082,\cdot)\) \(\chi_{4009}(1253,\cdot)\) \(\chi_{4009}(1519,\cdot)\) \(\chi_{4009}(1785,\cdot)\) \(\chi_{4009}(1823,\cdot)\) \(\chi_{4009}(2450,\cdot)\) \(\chi_{4009}(2507,\cdot)\) \(\chi_{4009}(2621,\cdot)\) \(\chi_{4009}(2678,\cdot)\) \(\chi_{4009}(2811,\cdot)\) \(\chi_{4009}(2982,\cdot)\) \(\chi_{4009}(3267,\cdot)\) \(\chi_{4009}(3647,\cdot)\) \(\chi_{4009}(3685,\cdot)\) \(\chi_{4009}(3913,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2111,1901)\) → \((-1,e\left(\frac{29}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{35}\right)\) |