Basic properties
Modulus: | \(2624\) | |
Conductor: | \(2624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 2624.eb
\(\chi_{2624}(259,\cdot)\) \(\chi_{2624}(339,\cdot)\) \(\chi_{2624}(395,\cdot)\) \(\chi_{2624}(403,\cdot)\) \(\chi_{2624}(427,\cdot)\) \(\chi_{2624}(475,\cdot)\) \(\chi_{2624}(507,\cdot)\) \(\chi_{2624}(627,\cdot)\) \(\chi_{2624}(931,\cdot)\) \(\chi_{2624}(1003,\cdot)\) \(\chi_{2624}(1019,\cdot)\) \(\chi_{2624}(1155,\cdot)\) \(\chi_{2624}(1195,\cdot)\) \(\chi_{2624}(1211,\cdot)\) \(\chi_{2624}(1219,\cdot)\) \(\chi_{2624}(1299,\cdot)\) \(\chi_{2624}(1571,\cdot)\) \(\chi_{2624}(1651,\cdot)\) \(\chi_{2624}(1707,\cdot)\) \(\chi_{2624}(1715,\cdot)\) \(\chi_{2624}(1739,\cdot)\) \(\chi_{2624}(1787,\cdot)\) \(\chi_{2624}(1819,\cdot)\) \(\chi_{2624}(1939,\cdot)\) \(\chi_{2624}(2243,\cdot)\) \(\chi_{2624}(2315,\cdot)\) \(\chi_{2624}(2331,\cdot)\) \(\chi_{2624}(2467,\cdot)\) \(\chi_{2624}(2507,\cdot)\) \(\chi_{2624}(2523,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{11}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(1299, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) |