Basic properties
| Modulus: | \(3407\) | |
| Conductor: | \(3407\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1703\) | 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 3407.g
\(\chi_{3407}(2,\cdot)\) \(\chi_{3407}(3,\cdot)\) \(\chi_{3407}(4,\cdot)\) \(\chi_{3407}(6,\cdot)\) \(\chi_{3407}(7,\cdot)\) \(\chi_{3407}(8,\cdot)\) \(\chi_{3407}(9,\cdot)\) \(\chi_{3407}(11,\cdot)\) \(\chi_{3407}(12,\cdot)\) \(\chi_{3407}(13,\cdot)\) \(\chi_{3407}(14,\cdot)\) \(\chi_{3407}(16,\cdot)\) \(\chi_{3407}(18,\cdot)\) \(\chi_{3407}(21,\cdot)\) \(\chi_{3407}(24,\cdot)\) \(\chi_{3407}(25,\cdot)\) \(\chi_{3407}(27,\cdot)\) \(\chi_{3407}(28,\cdot)\) \(\chi_{3407}(32,\cdot)\) \(\chi_{3407}(33,\cdot)\) \(\chi_{3407}(36,\cdot)\) \(\chi_{3407}(37,\cdot)\) \(\chi_{3407}(39,\cdot)\) \(\chi_{3407}(42,\cdot)\) \(\chi_{3407}(44,\cdot)\) \(\chi_{3407}(47,\cdot)\) \(\chi_{3407}(48,\cdot)\) \(\chi_{3407}(49,\cdot)\) \(\chi_{3407}(50,\cdot)\) \(\chi_{3407}(52,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1703})$ |
| Fixed field: | Number field defined by a degree 1703 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{2}{1703}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3407 }(625, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{1703}\right)\) | \(e\left(\frac{629}{1703}\right)\) | \(e\left(\frac{76}{1703}\right)\) | \(e\left(\frac{2}{1703}\right)\) | \(e\left(\frac{667}{1703}\right)\) | \(e\left(\frac{225}{1703}\right)\) | \(e\left(\frac{114}{1703}\right)\) | \(e\left(\frac{1258}{1703}\right)\) | \(e\left(\frac{40}{1703}\right)\) | \(e\left(\frac{911}{1703}\right)\) |