Basic properties
Modulus: | \(1031\) | |
Conductor: | \(1031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(103\) | 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.e
\(\chi_{1031}(10,\cdot)\) \(\chi_{1031}(15,\cdot)\) \(\chi_{1031}(26,\cdot)\) \(\chi_{1031}(29,\cdot)\) \(\chi_{1031}(32,\cdot)\) \(\chi_{1031}(39,\cdot)\) \(\chi_{1031}(48,\cdot)\) \(\chi_{1031}(49,\cdot)\) \(\chi_{1031}(72,\cdot)\) \(\chi_{1031}(88,\cdot)\) \(\chi_{1031}(100,\cdot)\) \(\chi_{1031}(106,\cdot)\) \(\chi_{1031}(107,\cdot)\) \(\chi_{1031}(108,\cdot)\) \(\chi_{1031}(115,\cdot)\) \(\chi_{1031}(119,\cdot)\) \(\chi_{1031}(132,\cdot)\) \(\chi_{1031}(133,\cdot)\) \(\chi_{1031}(137,\cdot)\) \(\chi_{1031}(150,\cdot)\) \(\chi_{1031}(159,\cdot)\) \(\chi_{1031}(162,\cdot)\) \(\chi_{1031}(188,\cdot)\) \(\chi_{1031}(198,\cdot)\) \(\chi_{1031}(211,\cdot)\) \(\chi_{1031}(215,\cdot)\) \(\chi_{1031}(217,\cdot)\) \(\chi_{1031}(225,\cdot)\) \(\chi_{1031}(226,\cdot)\) \(\chi_{1031}(242,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{103})$ |
Fixed field: | Number field defined by a degree 103 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{102}{103}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1031 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{103}\right)\) | \(e\left(\frac{12}{103}\right)\) | \(e\left(\frac{56}{103}\right)\) | \(e\left(\frac{28}{103}\right)\) | \(e\left(\frac{40}{103}\right)\) | \(e\left(\frac{74}{103}\right)\) | \(e\left(\frac{84}{103}\right)\) | \(e\left(\frac{24}{103}\right)\) | \(e\left(\frac{56}{103}\right)\) | \(e\left(\frac{7}{103}\right)\) |