Basic properties
Modulus: | \(206\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{103}(50,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 206.g
\(\chi_{206}(7,\cdot)\) \(\chi_{206}(15,\cdot)\) \(\chi_{206}(17,\cdot)\) \(\chi_{206}(19,\cdot)\) \(\chi_{206}(25,\cdot)\) \(\chi_{206}(29,\cdot)\) \(\chi_{206}(33,\cdot)\) \(\chi_{206}(41,\cdot)\) \(\chi_{206}(49,\cdot)\) \(\chi_{206}(55,\cdot)\) \(\chi_{206}(59,\cdot)\) \(\chi_{206}(63,\cdot)\) \(\chi_{206}(83,\cdot)\) \(\chi_{206}(91,\cdot)\) \(\chi_{206}(97,\cdot)\) \(\chi_{206}(105,\cdot)\) \(\chi_{206}(107,\cdot)\) \(\chi_{206}(119,\cdot)\) \(\chi_{206}(121,\cdot)\) \(\chi_{206}(129,\cdot)\) \(\chi_{206}(131,\cdot)\) \(\chi_{206}(135,\cdot)\) \(\chi_{206}(139,\cdot)\) \(\chi_{206}(141,\cdot)\) \(\chi_{206}(153,\cdot)\) \(\chi_{206}(155,\cdot)\) \(\chi_{206}(161,\cdot)\) \(\chi_{206}(163,\cdot)\) \(\chi_{206}(171,\cdot)\) \(\chi_{206}(185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\(5\) → \(e\left(\frac{23}{51}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 206 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) |