Basic properties
| Modulus: | \(8017\) | |
| Conductor: | \(8017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4008\) | 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 8017.s
\(\chi_{8017}(2,\cdot)\) \(\chi_{8017}(11,\cdot)\) \(\chi_{8017}(18,\cdot)\) \(\chi_{8017}(23,\cdot)\) \(\chi_{8017}(24,\cdot)\) \(\chi_{8017}(25,\cdot)\) \(\chi_{8017}(26,\cdot)\) \(\chi_{8017}(29,\cdot)\) \(\chi_{8017}(32,\cdot)\) \(\chi_{8017}(42,\cdot)\) \(\chi_{8017}(47,\cdot)\) \(\chi_{8017}(54,\cdot)\) \(\chi_{8017}(56,\cdot)\) \(\chi_{8017}(62,\cdot)\) \(\chi_{8017}(72,\cdot)\) \(\chi_{8017}(75,\cdot)\) \(\chi_{8017}(78,\cdot)\) \(\chi_{8017}(79,\cdot)\) \(\chi_{8017}(87,\cdot)\) \(\chi_{8017}(96,\cdot)\) \(\chi_{8017}(98,\cdot)\) \(\chi_{8017}(99,\cdot)\) \(\chi_{8017}(100,\cdot)\) \(\chi_{8017}(104,\cdot)\) \(\chi_{8017}(109,\cdot)\) \(\chi_{8017}(116,\cdot)\) \(\chi_{8017}(126,\cdot)\) \(\chi_{8017}(128,\cdot)\) \(\chi_{8017}(132,\cdot)\) \(\chi_{8017}(143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4008})$ |
| Fixed field: | Number field defined by a degree 4008 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1861}{4008}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8017 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{269}{2004}\right)\) | \(e\left(\frac{277}{501}\right)\) | \(e\left(\frac{269}{1002}\right)\) | \(e\left(\frac{1861}{4008}\right)\) | \(e\left(\frac{459}{668}\right)\) | \(e\left(\frac{409}{501}\right)\) | \(e\left(\frac{269}{668}\right)\) | \(e\left(\frac{53}{501}\right)\) | \(e\left(\frac{2399}{4008}\right)\) | \(e\left(\frac{1637}{2004}\right)\) |