Basic properties
Modulus: | \(103\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | 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 103.g
\(\chi_{103}(2,\cdot)\) \(\chi_{103}(4,\cdot)\) \(\chi_{103}(7,\cdot)\) \(\chi_{103}(15,\cdot)\) \(\chi_{103}(16,\cdot)\) \(\chi_{103}(17,\cdot)\) \(\chi_{103}(18,\cdot)\) \(\chi_{103}(19,\cdot)\) \(\chi_{103}(25,\cdot)\) \(\chi_{103}(26,\cdot)\) \(\chi_{103}(28,\cdot)\) \(\chi_{103}(29,\cdot)\) \(\chi_{103}(32,\cdot)\) \(\chi_{103}(33,\cdot)\) \(\chi_{103}(36,\cdot)\) \(\chi_{103}(38,\cdot)\) \(\chi_{103}(41,\cdot)\) \(\chi_{103}(49,\cdot)\) \(\chi_{103}(50,\cdot)\) \(\chi_{103}(52,\cdot)\) \(\chi_{103}(55,\cdot)\) \(\chi_{103}(58,\cdot)\) \(\chi_{103}(59,\cdot)\) \(\chi_{103}(60,\cdot)\) \(\chi_{103}(63,\cdot)\) \(\chi_{103}(68,\cdot)\) \(\chi_{103}(82,\cdot)\) \(\chi_{103}(83,\cdot)\) \(\chi_{103}(91,\cdot)\) \(\chi_{103}(92,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\(5\) → \(e\left(\frac{4}{51}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 103 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{40}{51}\right)\) |