Basic properties
| Modulus: | \(607\) | |
| Conductor: | \(607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(303\) | 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 607.g
\(\chi_{607}(2,\cdot)\) \(\chi_{607}(4,\cdot)\) \(\chi_{607}(9,\cdot)\) \(\chi_{607}(11,\cdot)\) \(\chi_{607}(13,\cdot)\) \(\chi_{607}(14,\cdot)\) \(\chi_{607}(15,\cdot)\) \(\chi_{607}(16,\cdot)\) \(\chi_{607}(18,\cdot)\) \(\chi_{607}(19,\cdot)\) \(\chi_{607}(22,\cdot)\) \(\chi_{607}(25,\cdot)\) \(\chi_{607}(28,\cdot)\) \(\chi_{607}(30,\cdot)\) \(\chi_{607}(32,\cdot)\) \(\chi_{607}(38,\cdot)\) \(\chi_{607}(41,\cdot)\) \(\chi_{607}(43,\cdot)\) \(\chi_{607}(50,\cdot)\) \(\chi_{607}(51,\cdot)\) \(\chi_{607}(52,\cdot)\) \(\chi_{607}(53,\cdot)\) \(\chi_{607}(61,\cdot)\) \(\chi_{607}(63,\cdot)\) \(\chi_{607}(71,\cdot)\) \(\chi_{607}(72,\cdot)\) \(\chi_{607}(73,\cdot)\) \(\chi_{607}(77,\cdot)\) \(\chi_{607}(79,\cdot)\) \(\chi_{607}(81,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{303})$ |
| Fixed field: | Number field defined by a degree 303 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{292}{303}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 607 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{242}{303}\right)\) | \(e\left(\frac{292}{303}\right)\) | \(e\left(\frac{181}{303}\right)\) | \(e\left(\frac{55}{303}\right)\) | \(e\left(\frac{77}{101}\right)\) | \(e\left(\frac{73}{101}\right)\) | \(e\left(\frac{40}{101}\right)\) | \(e\left(\frac{281}{303}\right)\) | \(e\left(\frac{99}{101}\right)\) | \(e\left(\frac{245}{303}\right)\) |