Basic properties
| Modulus: | \(1031\) | |
| Conductor: | \(1031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(515\) | 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 1031.g
\(\chi_{1031}(2,\cdot)\) \(\chi_{1031}(3,\cdot)\) \(\chi_{1031}(4,\cdot)\) \(\chi_{1031}(5,\cdot)\) \(\chi_{1031}(6,\cdot)\) \(\chi_{1031}(8,\cdot)\) \(\chi_{1031}(9,\cdot)\) \(\chi_{1031}(11,\cdot)\) \(\chi_{1031}(12,\cdot)\) \(\chi_{1031}(13,\cdot)\) \(\chi_{1031}(16,\cdot)\) \(\chi_{1031}(18,\cdot)\) \(\chi_{1031}(20,\cdot)\) \(\chi_{1031}(22,\cdot)\) \(\chi_{1031}(23,\cdot)\) \(\chi_{1031}(24,\cdot)\) \(\chi_{1031}(25,\cdot)\) \(\chi_{1031}(27,\cdot)\) \(\chi_{1031}(30,\cdot)\) \(\chi_{1031}(33,\cdot)\) \(\chi_{1031}(36,\cdot)\) \(\chi_{1031}(40,\cdot)\) \(\chi_{1031}(43,\cdot)\) \(\chi_{1031}(44,\cdot)\) \(\chi_{1031}(45,\cdot)\) \(\chi_{1031}(46,\cdot)\) \(\chi_{1031}(47,\cdot)\) \(\chi_{1031}(50,\cdot)\) \(\chi_{1031}(52,\cdot)\) \(\chi_{1031}(53,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{515})$ |
| Fixed field: | Number field defined by a degree 515 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{164}{515}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1031 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{249}{515}\right)\) | \(e\left(\frac{504}{515}\right)\) | \(e\left(\frac{498}{515}\right)\) | \(e\left(\frac{146}{515}\right)\) | \(e\left(\frac{238}{515}\right)\) | \(e\left(\frac{86}{103}\right)\) | \(e\left(\frac{232}{515}\right)\) | \(e\left(\frac{493}{515}\right)\) | \(e\left(\frac{79}{103}\right)\) | \(e\left(\frac{88}{515}\right)\) |