Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 1009.u
\(\chi_{1009}(37,\cdot)\) \(\chi_{1009}(128,\cdot)\) \(\chi_{1009}(134,\cdot)\) \(\chi_{1009}(200,\cdot)\) \(\chi_{1009}(201,\cdot)\) \(\chi_{1009}(251,\cdot)\) \(\chi_{1009}(288,\cdot)\) \(\chi_{1009}(300,\cdot)\) \(\chi_{1009}(334,\cdot)\) \(\chi_{1009}(432,\cdot)\) \(\chi_{1009}(449,\cdot)\) \(\chi_{1009}(501,\cdot)\) \(\chi_{1009}(508,\cdot)\) \(\chi_{1009}(560,\cdot)\) \(\chi_{1009}(577,\cdot)\) \(\chi_{1009}(675,\cdot)\) \(\chi_{1009}(709,\cdot)\) \(\chi_{1009}(721,\cdot)\) \(\chi_{1009}(758,\cdot)\) \(\chi_{1009}(808,\cdot)\) \(\chi_{1009}(809,\cdot)\) \(\chi_{1009}(875,\cdot)\) \(\chi_{1009}(881,\cdot)\) \(\chi_{1009}(972,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\(11\) → \(e\left(\frac{11}{72}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(128, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{72}\right)\) |